# Rocio Isabel PaezUniversity College Cork | UCC · School of Computer Science and Technology

Rocio Isabel Paez

PhD

## About

21

Publications

1,811

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

81

Citations

Citations since 2016

Introduction

I am currently a Senior Post-Doctoral Researcher for the FINTECHNEXT research group at UCC. My main research area is in Applied Mathematics, focusing on non-linear and complex dynamical systems, application of advanced methods of perturbation theory, high performance computations and characterization of dynamics of complex systems. Before Fintechnext, I worked as Postdoctoral researcher at the University of Padova and at RCAAM of the Academy of Athens.

Additional affiliations

July 2018 - present

July 2016 - June 2018

April 2016 - September 2016

## Publications

Publications (21)

The solutions originating at the Lagrangian points L1 and L2 of the restricted three-body problem are used in space flight dynamics to find useful station-keeping orbits as well as convenient low-energy transfers between planets and satellites of the Solar System. The circular restricted three-body problem (CR3BP) provides the simplest model where...

The halo orbits of the spatial circular restricted three-body problem are largely considered in space-flight dynamics to design low-energy transfers between celestial bodies. A very efficient analytical method for the computation of halo orbits, and the related transfers, has been obtained from the high-order resonant Birkhoff normal forms defined...

The halo orbits of the spatial circular restricted three-body problem are largely considered in space-flight dynamics to design low-energy transfers between celestial bodies. A very efficient analytical method for the computation of halo orbits, and the related transfers, has been obtained from the high-order resonant Birkhoff normal forms defined...

Starting with Arnold's pioneering work, the term "Arnold diffusion" has been used to describe the slow diffusion taking place in the space of the actions in Hamiltonian nonlinear dynamical systems with three or more degrees of freedom. The present text is an elaborated transcript of the introductory course given in the Milano I-CELMECH school on th...

In the last decades a peculiar family of solutions of the circular restricted three body problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit close to the Lagrangian points L 1 , L 2 of the CRTBP, have been classified using the values of approximate l...

In the last decades a peculiar family of solutions of the Circular Restricted Three Body Problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit close to the Lagrangian points $L_1,L_2$ of the CRTBP, have been classified using the values of approximate l...

Cornerstone models of physics, from the semi-classical mechanics in atomic and molecular physics to planetary systems, are represented by quasi-integrable Hamiltonian systems. Since Arnold’s example, the long-term diffusion in Hamiltonian systems with more than two degrees of freedom has been represented as a slow diffusion within the ‘Arnold web,’...

The dynamics near the Lagrange equilibria L1 and L2 of the Circular Restricted Three-body Problem has gained attention in the last decades due to its relevance in some topics such as the temporary captures of comets and asteroids and the design of trajectories for space missions. In this paper we investigate the temporary captures using the tube ma...

The normalizations of the Hamiltonian of the circular restricted three-body problem at a collinear Lagrange equilibrium are used to compute approximations of its center and tube manifolds, as well as of all the dynamics in their neighbourhood. For small values of the reduced mass m the radius of convergence of any (even partial) normalization at L1...

The manifold theory of barred-spiral structure provides a dynamical mechanism explaining how spiral arms beyond the ends of galactic bars can be supported by chaotic flows extending beyond the bar's corotation zone. We discuss its applicability to N-body simulations of secularly evolving barred galaxies. In these simulations, we observe consecutive...

The manifold theory of barred-spiral structure provides a dynamical mechanism explaining how spiral arms beyond the ends of galactic bars can be supported by chaotic flows extending beyond the bar's co-rotation zone. We discuss its applicability to N-body simulations of secularly evolving barred galaxies. In these simulations, we observe consecutiv...

Cornerstone models of Physics, from the semi-classical mechanics in atomic and molecular physics to planetary systems, are represented by quasi-integrable Hamiltonian systems. Since Arnold's example, the long-term diffusion in Hamiltonian systems with more than two degrees of freedom has been represented as a slow diffusion within the `Arnold web',...

One of the most interesting features in the libration domain of co-orbital motions is the existence of secondary resonances. For some combinations of physical parameters, these resonances occupy a large fraction of the domain of stability and rule the dynamics within the stable tadpole region. In this work, we present an application of a recently i...

A number of studies, referring to the observed Trojan asteroids of various planets in our Solar System, or to hypothetical Trojan bodies in extrasolar planetary systems, have emphasized the importance of so-called secondary resonances in the problem of the long term stability of Trojan motions. Such resonances describe commensurabilities between th...

The main subject of this work is the study of the problem of the Trojan orbits from a perturbative Hamiltonian perspective. We face this problem by introducing first a novel Hamiltonian formulation, exploiting the well-differentiated temporal scales of the Trojan motion. The resulting Hamiltonian allows to separate the secular (very slow) component...

The study of the Trojan problem (i.e. the motion in the vicinity of the equilateral Lagrangian points L
4 or L
5) has a long history in the literature. Starting from a representation of the Elliptic Restricted 3-Body Problem in terms of modified Delaunay variables, we propose a sequence of canonical transformations leading to a Hamiltonian decompos...

In this work, we study the motions in the region around the equilateral Lagrangian equilibrium points L
4 and L
5, in the framework of the Circular Planar Restricted Three-Body Problem (hereafter, CPRTBP). We design a semi-analytic approach based on some ideas by Garfinkel in [4]: the Hamiltonian is expanded in Poincaré-Delaunay coordinates and a s...

We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework
of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some
sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniq...

In the framework of the ERTBP, we study an example of the influence of
secondary resonances over the long term stability of Trojan motions. By the
integration of ensembles of orbits, we find various types of chaotic diffusion,
slow and fast. We show that the distribution of escape times is bi-modular,
corresponding to two populations of short and l...

We investigate the dynamics of small trojan exoplanets in domains of
secondary resonances within the tadpole domain of motion. We consider the limit
of a massless trojan companion of a giant planet. Without other planets, this
is a case of the elliptic restricted three body problem (ERTBP). The presence
of more planets (the restricted multi-planet...

We consider the dynamics of a small trojan companion of a hypothetical giant
exoplanet under the secular perturbations of additional planets. By a suitable
choice of action-angle variables, the problem is amenable to the study of the
slow modulation, induced by secular perturbations, to the dynamics of an
otherwise called `basic' Hamiltonian model...

## Projects

Projects (2)

The aim of the Training School is to present a contemporary review of recent results in the field of Celestial Mechanics. Special emphasis will be placed on the theoretical aspects.
REGISTRATION DEADLINE: OCTOBER 30, 2019
See our webpage:
http://www.mat.unimi.it/I-CELMECH/index.php/training-school/

9th Humboldt Colloquium on Celestial Mechanics taking place in Bad Hofgastein, Austria: https://avhc9.wordpress.com/ from 19-25.03.2017.
50 great scientists from all over the world meet together in Austria to discuss new scientific results in Astronomy and Space Sciences.