Related papers: A new dynamical indicator for chaos detection in g…
We investigate the chaotic dynamics of the massless test particles moving in the regular black hole supported by a Dehnen-type dark matter halo. By limiting the particle within a external harmonic potential, we employ Poincar\'e sections…
Depending on initial conditions, individual finite time trajectories of dynamical systems can have very different chaotic properties. Here we present a numerical method to identify trajectories with atypical chaoticity, pathways that are…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…
The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in…
Together with the variational indicators of chaos, the spectral analysis methods have also achieved great popularity in the field of chaos detection. The former are based on the concept of local exponential divergence. The latter are based…
We apply the Smaller ALignment Index (SALI) method to a 4--dimensional mapping of accelerator dynamics in order to distinguish rapidly, reliably and accurately between ordered and chaotic motion. The main advantage of this index is that it…
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
We revisit the global dynamics of unified dark matter cosmological models and analyze it in a new dynamical system setting. In particular, by defining a suitable set of variables we obtain a bounded variable space, a feature that allows a…
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small…
The decay of the overlap between a wave packet evolved with a Hamiltonian H and the same state evolved with H}+$\Sigma $ serves as a measure of the decoherence time $\tau_{\phi}$. Recent experimental and analytical evidence on classically…
A new universality of Lyapunov spectra {\lambda_i} is shown for Hamiltonian systems. The universality appears in middle energy regime and is different from another universality which can be reproduced by random matrices in the following two…
We investigate localization phenomena and stability properties of quasiperiodic oscillations in $N$ degree of freedom Hamiltonian systems and $N$ coupled symplectic maps. In particular, we study an example of a parametrically driven…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a…
We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas…