Matheus Palmero

• Doctor in Physics
• University of São Paulo

In this work we investigate how the behavior of the Shannon entropy can be used to measure the diffusion exponent of a set of initial conditions in two systems: (i) standard map and (ii) the oval billiard. We are interested in the diffusion near the main island in the phase space, where stickiness is observed. We calculate the diffusion exponent fo...

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in a phase space, the method of images, and the use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with...

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov–Taylor Standard Map. We show that trajectories started from special initial conditions, close to unstable periodic orbits, exhibit sub-diffusion due to stickiness, and can be modeled as a continuous-time random walk. Additionally, we choose a variant of the Ulam met...

Hamiltonian systems that are either open, leaking, or contain holes in the phase space possess solutions that eventually escape the system’s domain. The motion described by such escape orbits before crossing the escape threshold can be understood as a transient behavior. In this work, we introduce a numerical method to visually illustrate and quant...

In this work, we show that a finite-time recurrence analysis of different chaotic trajectories in two-dimensional non-linear Hamiltonian systems provides useful prior knowledge of their dynamical behavior. By defining an ensemble of initial conditions, evolving them until a given maximum iteration time, and computing the recurrence rate of each orb...

Predicting and characterizing diverse non-linear behaviors in dynamical systems is a complex challenge, especially due to the inherently presence of chaotic dynamics. Current forecasting methods are reliant on system-specific knowledge or heavily parameterized models, which can be associated with a variety of drawbacks including critical model assu...

In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the complete understanding of the complex dynamical evolution of chaotic trajectories is a challenge that, when o...

Chaotic transport is related to the complex dynamical evolution of chaotic trajectories in Hamiltonian systems, which models various physical processes. In magnetically confined plasma, it is possible to qualitatively describe the configuration of the magnetic field via the phase space of suitable symplectic maps. These phase spaces are of mixed ty...

In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the complete understanding of the chaotic transport is a challenge that, when overcome, may provide further knowl...

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time Random Walk model and connected to the theoretical background for anomalous diffusion. Additionally, we choose a...

In this work, we introduce the escape measure, a finite-time version of the natural measure, to investigate the transient dynamics of escape orbits in open Hamiltonian systems. In order to numerically calculate the escape measure, we cover a region of interest of the phase space with a grid and we compute the visitation frequency of a given orbit o...

We investigate how the diffusion exponent is affected by controlling small domains in the phase space.The main Kolomogorov-Arnold-Moser - KAM island of the Standard Map is considered to validate the investigation. The bifurcation scenario where the periodic island emits smaller resonance regions is considered and we show how closing paths escape fr...

Mushroom billiards are formed, generically, by a semicircular hat attached to a rectangular stem. The dynamics of mushroom billiards shows a continuous transition from integrability to chaos. However, between those limits the phase space is sharply divided in two components corresponding to regular and chaotic orbits, in contrast to most mixed phas...

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in phase space, the method of images and use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with chaoti...

The dynamics of an ensemble of non-interacting particles suffering elastic collisions inside a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. The system presents a resonance velocity, which plays an important role on the ensemble separation according to the initial velocities. The idea is to use the Lyapu...

We study the dynamics of an ensemble of non interacting particles constrained by two infinitely heavy walls, where one of them is moving periodically in time, while the other is fixed. The system presents mixed dynamics, where the accessible region for the particle to diffuse chaotically is bordered by an invariant spanning curve. Statistical analy...

A competition between decay and growth of energy in a time-dependent stadium billiard is discussed. The dynamics of an ensemble of non-interacting particles inside a closed domain in the shape of a stadium is described by the use of a four-dimensional non-linear mapping. A critical resonance velocity is identified for causing of separation between...