# G. VoyatzisAristotle University of Thessaloniki | AUTH · Division of Physics (PHYS)

G. Voyatzis

Professor

## About

104

Publications

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1,900

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Introduction

Dynamics - Celestial Mechanics

## Publications

Publications (104)

We study the motion of an asteroid being in retrograde 1/1 resonance with Jupiter (co-orbital motion). We consider the planar case (i=180°) and Jupiter is on a circular or elliptic orbit ( e ′ = 0.048). In the cirular model we compute families of symmetric periodic orbits and their stability type. In the elliptic model we have isolated periodic orb...

We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system's evolution after deflection by a kinetic impactor. To this end, both a linear and nonlinear (canonical) theory are developed. We make the...

We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system’s evolution after deflection by a kinetic impactor. To this end, both linear and nonlinear (canonical) theories are developed. We make the...

We compute planar and three-dimensional retrograde periodic orbits in the vicinity of the restricted three-body problem (RTBP) with the Sun and Neptune as primaries and we concentrate on the dynamics of higher-order exterior mean motion resonances with Neptune. By using the circular planar model as the basic model, families of retrograde symmetric...

Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that introduce chaos into the evolution of the system on especially shorter or longer timescales. We propose a study o...

Aims. Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that introduce chaos into the evolution of the system on especially shorter or longer timescales. We propose a s...

We study the dynamics of interior mean motion resonances of first, second and third order with Jupiter using the model of the restricted three-body problem with the Sun and Jupiter as primaries and we focus on asteroids which are in retrograde motion with the perturbing planet. The basis of our study is the computation of three-dimensional symmetri...

In Karydis et al (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravita-tional field of an irregularly-shaped asteroid starting from a symmetric simple model. What's more, we map the families of periodic orbits of the simple model to families of the real asteroid model. The introduction...

In Karydis et al. (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravitational field of an irregularly-shaped asteroid starting from a symmetric simple model. What’s more, we map the families of periodic orbits of the simple model to families of the real asteroid model. The introduction...

The orbital dynamics in the gravitational environment of irregular asteroids is an important issue for space missions and a quite complex problem. In this paper we propose a methodological approach for computing periodic orbits around rotating, irregular-shaped asteroids. Our study starts from the families of periodic orbits of a triaxial ellipsoid...

We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 10-3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-3}$$\en...

We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 0.001, analyzing their stability and bifurcations into 3-dimensional periodic orbits. We explain the role played by periodic orbits in adiabatic resonance capture, in particular how the proximity between a stable family and an unstable family wit...

We study planar and three-dimensional retrograde periodic orbits, using the model of the restricted three-body problem (RTBP) with the Sun and Neptune as primaries and focusing on the dynamics of resonant trans-Neptunian objects (TNOs). The position and the stability character of the periodic orbits can provide important piece of information on the...

We study planar resonant retrograde periodic orbits, using the model of the restricted three-body problem with the Sun and Jupiter as primaries. The position and the stability character of the periodic orbits are very useful for the study of the phase space structure and this will provide important piece of information on the stability and long ter...

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the rel...

The stability of gravitational triple systems is a well-known problem in celestial mechanics. The basic model used is the general three body problem (GTBP). Many criteria estimated from the integrals of motion and zero velocity curves or from purely numerical simulations have been given in literature. In this paper, we propose a different approach...

In this paper, we study the long-term dynamical evolution of highly elliptical orbits in the medium-Earth orbit region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrati...

Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is known that quasi-satellite motion is associated with a family of periodic solutions, called family f, which consis...

Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is known that quasi-satellite motion is associated with a family of periodic solutions, called family $f$, which cons...

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term (120 years) integrations of the...

Librational motion in celestial mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or $\pi$, the libration is called asymmetric. In the co...

The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the primaries is assumed to be a non-singular point. The rectilinear model has been proposed as a starting model for stud...

Space debris mitigation is one of the most important problems of space science and applications. In this work, we present our recent investigations on the possibility of exploiting the natural long-term dynamics of artificial satellites and debris to address the problem of designing passive mitigation strategies. Our work consists of the characteri...

We consider planetary systems evolving under the effect of a Stokes-type dissipative force mimicking the outcome of a type II migration process. As inward migration proceeds and the planets follow the circular family (they start on circular orbits) and even though they are initially almost coplanar, resonance capture can be realized. Then, at the \...

Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of periodic orbits for planetary systems. The study is restricted to coplanar motion. Staring from known results...

We present a numerical investigation of the coupled gravitational and nongravitational perturbations acting on Earth satellite orbits in the whole circumterrestrial space, using a suitably modified version of the SWIFT symplectic integration package. We characterize the dynamical architecture of the Earth-orbiting environment from low-Earth orbits...

The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly eccentric. In these cases, in order for close encounters, which destabilize the planetary systems, to be avoided, phase...

Migration of planetary systems caused by the action of dissipative forces may lead the planets to be trapped in a resonance. In this work we study the conditions and the dynamics of such resonant trapping. Particularly, we are interested in finding out whether resonant capture ends up in a long-term stable planetary configuration. For two planet sy...

Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem as our model. Highly eccentric orbits are out of the Hill stability regions. However, mean motion resonances...

We herein utilize the general three-body problem (GTBP) as a model, in order
to simulate resonant systems consisting of a star and two planets, where at
least one of them is highly eccentric. We study them in terms of their
long-term stability, via the construction of maps of dynamical stability and
the computation of the corresponding families of...

In dynamical systems of few degrees of freedom, periodic solutions consist
the backbone of the phase space and the determination and computation of their
stability is crucial for understanding the global dynamics. In this paper we
study the classical three body problem in three dimensions and use its dynamics
to assess the long-term evolution of ex...

We consider a two-planet system, which migrates under the influence of
dissipative forces that mimic the effects of gas-driven (Type II) migration. It
has been shown that, in the planar case, migration leads to resonant capture
after an evolution that forces the system to follow families of periodic
orbits. Starting with planets that differ slightl...

We study the dynamics of a two-planet system, which evolves being in a $1/1$
mean motion resonance (co-orbital motion) with non-zero mutual inclination. In
particular, we examine the existence of bifurcations of periodic orbits from
the planar to the spatial case. We find that such bifurcations exist only for
planetary mass ratios $\rho=\frac{m_2}{...

In this work we use standard Hamiltonian-system techniques in order to study the dynamics of three vortices with alternating charges in a confined Bose-Einstein condensate. In addition to being motivated by recent experiments, this system offers a natural vehicle for the exploration of the transition of the vortex dynamics from ordered to progressi...

In this work we use standard Hamiltonian-system techniques in order to study the dynamics of three vortices with alternating charges in a confined Bose-Einstein condensate. In addition to being motivated by recent experiments, this system offers a natural vehicle for the exploration of the transition of the vortex dynamics from ordered to progressi...

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion
resonances is studied by using the model of the general three body problem in a
rotating frame and by determining families of periodic orbits for each
resonance. Both planar and spatial cases are examined. In the spatial problem
families of periodic orbits are obtained after...

Over the last decades, there has been a tremendous increase in research on
extrasolar planets. Many exosolar systems, which consist of a Star and two
inclined Planets, seem to be locked in 4/3, 3/2, 2/1, 5/2, 3/1 and 4/1 mean
motion resonance (MMR). We herewith present the model used to simulate three
dimensional planetary systems and provide plana...

We consider systems composed of two giant planets, which migrate
radially due to their interaction with their host protoplanetary disc,
in an effort to understand under which conditions '3-D' resonant systems
can form. Planet migration can lead to permanent resonant capture and,
in the planar case, it has been shown that the planets evolves along
f...

Many exo-solar systems discovered in the last decade consist of planets
orbiting in resonant configurations and consequently, their evolution should
show long-term stability. However, due to the mutual planetary interactions a
multi-planet system shows complicated dynamics with mostly chaotic
trajectories. We can determine possible stable configura...

Discoveries of exoplanets orbiting evolved stars motivate critical examinations of the dynamics of N-body systems with mass-loss. Multiplanet evolved systems are particularly complex because of the mutual interactions between
the planets. Here, we study the underlying dynamical mechanisms which can incite planetary escape in two-planet post-main-se...

Discoveries of exoplanets orbiting evolved stars motivate critical
examinations of the dynamics of $N$-body systems with mass loss. Multi-planet
evolved systems are particularly complex because of the mutual interactions
between the planets. Here, we study the underlying dynamical mechanisms which
can incite planetary escape in two-planet post-main...

GAIA is expected to greatly enhance our knowledge on the orbital, spin-state, spectral and size distribution of individual asteroids and asteroid families. Dynamical models, incorporating resonant phenomena and thermal (Yarkovsky/YORP) effects, can be used to understand the observations, in particular the orbital, size-frequency and spin-axis distr...

We consider the general spatial three body problem and study the dynamics of
planetary systems consisting of a star and two planets which evolve into 2/1
mean motion resonance and into inclined orbits. Our study is focused on the
periodic orbits of the system given in a suitable rotating frame. The stability
of periodic orbits characterize the evol...

The motion of a satellite around a planet can be studied by the Hill model,
which is a modification of the restricted three body problem pertaining to
motion of a satellite around a planet. Although the dynamics of the circular
Hill model have been extensively studied in the literature, only few results
about the dynamics of the elliptic model were...

We study the evolution of a conservative dynamical system with three degrees of freedom, where small nonconservative terms are added. The conservative part is a Hamiltonian system, describing the motion of a planetary system consisting of a star, with a large mass, and of two planets, with small but not negligible masses, that interact gravitationa...

We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only in particular resonances called "asymmetric resonances". However, numerical studies showed that in the genera...

We present families of symmetric and asymmetric periodic orbits at the 1/1
resonance, for a planetary system consisting of a star and two small bodies, in
comparison to the star, moving in the same plane under their mutual
gravitational attraction. The stable 1/1 resonant periodic orbits belong to a
family which has a planetary branch, with the two...

We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two
planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different laws of friction
are considered. The topology of the phase space is essential in understanding the evolution of t...

We investigate the rotational dynamics of a triaxial planet moving on a Keplerian orbit around its star. The dynamics is ruled
by several parameters, like the eccentricity, the obliquity, the non-principal rotation, the angular momentum, etc. We consider
two specific cases in which the planet is symmetric or asymmetric, according to whether two mom...

The continuation of resonant periodic orbits from the restricted to the general three body problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular restricted problem. Then we find all the families of the resonant elliptic restricted three body problem which bifurcate fro...

We study orbits of planetary systems with two planets, for planar motion, at the 1/1 resonance. This means that the semimajor
axes of the two planets are almost equal, but the eccentricities and the position of each planet on its orbit, at a certain
epoch, take different values. We consider the general case of different planetary masses and, as a s...

The 2/1 resonant dynamics of a two-planet planar system is studied within the framework of the three-body problem by computing families of periodic orbits and their linear stability. The continuation of resonant periodic orbits from the restricted to the general problem is studied in a systematic way. Starting from the Keplerian unperturbed system,...

We study the factors that affect the stability and the long term evolution of a resonant planetary system. For the same resonance, the long term evolution of a resonant planetary system depends on the the relative orientation of the planetary orbits, on the phase of the planets on their orbits and on the proximity to a periodic resonant planetary s...

This study addresses the long-term evolution of possible two-planet extrasolar systems that are initially trapped in 3:1 mean motion resonance. A planar general three-body problem model is used, and its resonant dynamics are examined by computing periodic orbits in a rotating frame, Poincaré maps, and maps of dynamical stability. We computed the fa...

The dynamics of the Kuiper Belt region between 33 and 63 au is investigated just taking into account the gravitational influence
of Neptune. Indeed the aim is to analyse the information which can be drawn from the actual exoplanetary systems, where typically
physical and orbital data of just one or two planets are available. Under this perspective...

We study the dynamics at the 4:5 exterior mean motion resonance using the model of the restricted three-body problem with the Sun and Neptune as primaries. The position and the stability character of the periodic orbits determine critically the structure of the phase space and particularly the qualitative characteristics of the long-term evolution...

We study the dynamics of 3:1 resonant motion for planetary systems with two planets, based on the model of the general planar
three body problem. The exact mean motion resonance corresponds to periodic motion (in a rotating frame) and the basic families
of symmetric and asymmetric periodic orbits are computed. Four symmetric families bifurcate from...

The acceleration of charged particles in the presence of a magnetic field and gravitational waves is under consideration. It is shown that the weak gravitational waves can cause the acceleration of low energy particles under appropriate conditions. Such conditions may be satisfied close to the source of the gravitational waves if the magnetized pla...

In the framework of the three dimensional restricted three-body problem we study the dynamics of the exterior mean motion resonances with Neptune. The basis of our study is the computation of periodic orbits and their linear stability. The position and stability of periodic orbits critically determine the phase space topology. Stable periodic orbit...

In the framework of the planar restricted three-body problem we study a considerable number of resonances associated to the basic dynamical features of Kuiper belt and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic orbits and their stability. Stable periodic orbits are surrounded by regular librations in p...

Families of asymmetric periodic orbits at the 2/1 resonance are computed for different mass ratios. The existence of the asymmetric
families depends on the ratio of the planetary (or satellite) masses. As models we used the Io-Europa system of the satellites
of Jupiter for the case m1>m2, the system HD82943 for the new masses, for the case m1=m2 an...

In the framework of the restricted three body problem, the resonant periodic orbits associated with the Kuiper belt dynamics are studied. Particularly, all the first, second and third order exterior mean motion resonances with Neptune located up to 50A.U. and the asymmetric resonances (beyond the 48 A.U.) are considered. We present the bifurcation...

We present families of periodic orbits and their stability for the exterior mean motion resonances 1:2, 1:3 and 1:4 with Neptune
in the framework of the planar circular restricted three-body problem. We found that in each resonance there exist two branches
of symmetric elliptic periodic orbits with stable and unstable segments. Asymmetric periodic...

In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic orbits and their stability. Stable periodic orbits are surrounded by regular librations in phase space and in s...

We present the families of periodic orbits and their stability for the exterior mean motion resonances 1/2, 1/3 and 1/4 with Neptune in the framework of the planar circular restricted three-body problem. We found that in each resonance there exist two branches of elliptic orbits with stable and unstable segments. Asymmetric periodic orbits bifurcat...

The 2:3 and 3:4 exterior mean motion resonances with Neptune are studied by applying symplectic mapping models. The mappings
represent efficiently Poincaré maps for the 3D elliptic restricted three body problem in the neighbourhood of the particular
resonances. A large number of trajectories is studied showing the coexistence of regular and chaotic...

We investigate the non-linear interaction of a strong gravitational wave with the plasma during the collapse of a massive magnetized star to form a black hole, or during the merging of neutron star binaries. We find that under certain conditions this coupling may result in an efficient energy space diffusion of particles. We suggest that the atmosp...

We investigate the non-linear interaction of a strong Gravitational Wave with the plasma during the collapse of a massive magnetized star to form a black hole, or during the merging of neutron star binaries (central engine). We found that under certain conditions this coupling may result in an efficient energy space diffusion of particles. We sugge...

We consider the problem of trajectory classification (as regular or chaotic) in Hamiltonian systems through power spectrum
analysis. We focus our attention on the low frequency domain and we study the asymptotic behavior of the power spectrum when
the frequencies tend to zero. A low frequency power estimator γ is derived that indicates the signific...

The overlapping of isochronous resonances of non-twist Hamiltonian systems can be studied by considering integrable models which result in a smooth reconnection of the homoclinic and heteroclinic manifolds. A complex net of separatrices is formed that depends on the number of the overlapped resonances and their characteristic type. One degree of fr...

In this Letter we consider n degrees-of-freedom integrable Hamiltonian systems subjected to a non-Hamiltonian perturbation controlled by a small parameter ε. An obstruction to the analytic continuation of the integrals of motion of the unperturbed system with respect to ε is developed for sufficiently small perturbations. The theory is applied to a...

A comparative study is made between the 2/1 and the 3/2 resonant asteroid motion, with the aim to understand their different behaviour (gap in the 2/1 resonance, group in the 3/2 resonance). A symplectic mapping model is used, for each of these two resonances, assuming the asteroid is moving in the three-dimensional space under the gravitational pe...

this article we studied the copyright protection of digital still images through invisible watermarking. Watermarking schemes serve for searching in the global network for illegal copies of digital products and for providing reliable indications or proofs for copyright ownership.

The watermarking of digital images, audio, video, and multimedia
products in general has been proposed for resolving copyright ownership
and verifying originality of content. This paper studies the
contribution of watermarking for developing protection schemes. A
general watermarking framework (GWF) is studied and the fundamental
demands are listed...

The digital networked environment necessitates the development of protection techniques for multimedia product access and distribution. This paper refers to protection schemes for copyright and content originality of multimedia products through invisible watermarking. In particular, we present the basic protection schemes and fundamental concepts....

The twist condition is a necessary condition in integrable Hamiltonian systems and symplectic maps to obtain Poincaré-Birkhoff bifurcations under small perturbations. When this condition does not hold, topological structures other than Poincaré-Birkhoff chains arise in phase space through bifurcations of isolated periodic orbits and reconnections o...

Digital watermarks offer a way to counter copyright piracy on the
global network. We summarize the fundamental concepts of watermarking
and describe a general framework for a copyright protection system.
Watermarks efficiently protect copyright when basic demands can be
satisfied. However, the demand for watermarks to remain robust under
digital im...

Transmission, manipulation and storage of images in digital format is rapidly becoming an everyday practice. Desktop publishing, digital libraries, image databases and the World Wide Web are only some of the application areas that are strongly related to digital imaging technology. The new digital, networked environment necessitates the development...

Spectral properties associated with the deformation of tori and the transition to chaos in near-integrable Hamiltonian systems are studied. Information about the construction of tori is provided by studying the evolution of the integrals of the unperturbed system when a perturbation is added. The authors show that the low band of the power spectrum...

In this paper an Automatic System for Image Digital Capturing (ASIDC) is described. The aim of ASIDC is to create high resolution digital images depicting paintings of large size. The system creates a set of N digital images presenting sequential frames of the total picture. By using software we proceed to the mosaicing (pasting) of the images prod...

This paper presents a watermarking scheme for copyright protection of digital images. A binary logo is the copyright label which is embedded in grayscale or color digital images. A set of integer parameters, selected by the legal owner, controls the watermarking algorithm via a strongly chaotic (mixing) system. Watermark detection is performed with...

In this paper we describe a general framework for image copyright protection through digital watermarking. In particular we present the main features of an efficient watermarking scheme, discuss robustness issues and describe the three main stages of a watermarking algorithm namely watermark generation, embedding and detection. 1 INTRODUCTION The r...

This paper presents a watermarking algorithm for copyright
protection of digital images. A copyright label represented by a binary
image is embedded in grayscale or color digital image. A mixing
dynamical system controls embedding, detection and reconstruction of the
copyright label. Detection of the watermark is succeeded either by
direct reconstr...

Digital watermarking methods have been proposed for various
purposes and especially for copyright protection of multimedia data. The
digital watermark is embedded in a digital signal or an image and must
be unrecognizable by unauthorized persons and detectable only by the
legal copyright owner. We use toral automorphisms as chaotic 2-D integer
vect...

We consider spatially uniform SU(2) color fields. At the classical level the system exhibits almost exclusively chaotic behavior. To include quantum effects, we introduce a renormalization-group-improved effective action, where the fixed coupling constant g is replaced by a running coupling constant g¯, depending upon the color magnetic field. The...

The evolution of the eccentricity of particular asteroidal trajectories
in the 2:1 resonance is analysed by a spectral scheme. This analysis is
an alternative to the well known analysis based on the computation of
Liapunov exponents. The method can be used to estimate the long time
evolution of a trajectory from a segment considerably shorter than...

We report here recent work on the long term evolution of an asteroid near the 3:1 resonance with Jupiter, for planar motion, by making use of a mapping model (Hadjidemetriou, 1993). Some additional results are also included. The mapping is four dimensional and is a model for the Poincaré mapping, on a surface of section, of the elliptic restricted...

An apparent connection between integrability and the existence of a periodic solution of the variational equations around the straight-line solutions of planar Hamiltonian systems has been suggested [F. T. Hioe, Phys. Rev. A 39, 2628 (1989)]. Such solutions always exist if the gradient of the second integral and the Hamiltonian are independent on t...