相关论文: Dynamics and Statistics of Weak Chaos in a 4--D Sy…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…

In this work, we study a family of fully chaotic billiards that exhibits only rotational symmetries, whose geometry is based on the $C_3$ symmetry system proposed by Leyvraz, Schmit, and Seligman~(LSS) in 1996. Quantum spectral analyses are…

Initially, the logistic map became popular as a simplified model for population growth. In spite of its apparent simplicity, as the population growth-rate is increased the map exhibits a broad range of dynamics, which include bifurcation…

We investigate the effects of classical stickiness (orbits temporarily confined to a region of the chaotic phase space) to the structures of the quantum states of an open system. We consider the standard map of the kicked rotor and verify…

Understanding the dynamics of multi--dimensional conservative dynamical systems (Hamiltonian flows or symplectic maps) is a fundamental issue of non-linear science. The Generalized ALignment Index (GALI), which was recently introduced and…

We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular,…

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories…

We introduce, and numerically study, a system of $N$ symplectically and globally coupled standard maps localized in a $d=1$ lattice array. The global coupling is modulated through a factor $r^{-\alpha}$, being $r$ the distance between maps.…

We define auto- and cross-correlation functions capable to capture dynamical characteristics induced by local phase space structures in a general dynamical system. These correlation functions are calculated in the Standard Map for a range…

In the study of subdiffusive wave-packet spreading in disordered Klein-Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as…

Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…

Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…

A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…

The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the…

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…

This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…

In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a nontrival homoclinic class that is not uniformly hyperbolic or the diffeomorphism is a $C^{1+\alpha}$ and there is a hyperbolic ergodic…

Everything you ever wanted to know about what has come to be known as ``chaotic mixing:'' This paper describes the evolution of localised ensembles of initial conditions in 2- and 3-D time-independent potentials which admit both regular and…