Statistical mechanical characterization of billiard systems

K Cetin, U Tirnakli, DFM Oliveira, ED Leonel - Chaos, Solitons & Fractals, 2024 - Elsevier
Area-preserving maps play an important role in diverse fields as they are widely used for
modeling complex systems. In addition, these maps provide rich observations by presenting …

A generalization of the standard map and its statistical characterization

K Cetin, U Tirnakli, BM Boghosian - Scientific Reports, 2022 - nature.com
From the statistical mechanical point of view, area-preserving maps have great potential and
importance. These maps exhibit chaotic and regular behavior separately or together in the …

Visualization and comparison of classical structures and quantum states of four-dimensional maps

M Richter, S Lange, A Bäcker, R Ketzmerick - Physical Review E, 2014 - APS
For generic 4D symplectic maps we propose the use of 3D phase-space slices, which allow
for the global visualization of the geometrical organization and coexistence of regular and …

Distance correlation detecting Lyapunov instabilities, noise-induced escape times and mixing

CFO Mendes, MW Beims - Physica A: Statistical Mechanics and its …, 2018 - Elsevier
The properties of the statistical method of distance correlation between multivariate data are
analysed in the context of nonlinear dynamical systems. The distance correlation between …

Characterizing weak chaos using time series of Lyapunov exponents

RM Da Silva, C Manchein, MW Beims, EG Altmann - Physical Review E, 2015 - APS
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the
finite-time Lyapunov exponents. The methodology we propose uses the number of …

The influence of hyperchaoticity, synchronization, and Shannon entropy on the performance of a physical reservoir computer

LAS Rosa, EL Brugnago, GJ Delben, JM Rost… - … Journal of Nonlinear …, 2024 - pubs.aip.org
In this paper, we analyze the dynamic effect of a reservoir computer (RC) on its performance.
Modified Kuramoto's coupled oscillators are used to model the RC, and synchronization …

Finite-time Lyapunov fluctuations and the upper bound of classical and quantum out-of-time-ordered expansion rate exponents

MA Prado Reynoso, GJ Delben, M Schlesinger… - Physical Review E, 2022 - APS
This Letter demonstrates for chaotic maps [logistic, classical, and quantum standard maps
(SMs)] that the exponential growth rate (Λ) of the out-of-time-ordered four-point correlator is …

Characterizing weak chaos in nonintegrable Hamiltonian systems: The fundamental role of stickiness and initial conditions

C Manchein, MW Beims, JM Rost - Physica A: Statistical Mechanics and its …, 2014 - Elsevier
Weak chaos in high-dimensional conservative systems can be characterized through sticky
effect induced by invariant structures on chaotic trajectories. Suitable quantities for this …

Weak dissipative effects on trajectories from the edge of basins of attraction

CA Jousseph, TS Kruger, C Manchein… - Physica A: Statistical …, 2016 - Elsevier
The purpose of this work is to present convergence properties of regular and chaotic
conservative trajectories under small dissipation. It is known that when subjected to …

Power-law trap** in the volume-preserving Arnold-Beltrami-Childress map

S Das, A Bäcker - Physical Review E, 2020 - APS
Understanding stickiness and power-law behavior of Poincaré recurrence statistics is an
open problem for higher-dimensional systems, in contrast to the well-understood case of …