Related papers: A simple non-chaotic map generating subdiffusive, …
In the present paper, we give a series of definitions and properties of Lifting Dynamical Systems (LDS) corresponding to the notion of deterministic diffusion. We present heuristic explanations of the mechanism of formation of deterministic…
Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic…
A statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards, one with mushroom-like shape and the other from the familiy of the Limacon billiards, is presented. These billiards have mixed…
We adapt ideas from geometrical optics and classical billiard dynamics to consider particle trajectories with constant velocity on a cone with specular reflections off an elliptical boundary formed by the intersection with a tilted plane,…
In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard…
We construct nontrivial deformations of the standard map which preserve the symplectic actions, respectively the Lyapunov exponents, of infinitely many periodic orbits accumulating to an invariant curve. The proof uses a resonant…
Chaotic deterministic dynamics of a particle can give rise to diffusive Brownian motion. In this paper, we compute analytically the diffusion coefficient for a particular two-dimensional stochastic layer induced by the kicked Harper map.…
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…
Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive (collision) forces. When it is desired or necessary to account for linear/angular momentum exchange…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values…
Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide…
We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. We give new results on periodicity and boundedness of orbits which suggest…
We present a semiclassical theory for transport through open billiards of arbitrary convex shape that includes diffractively scattered paths at the lead openings. Starting from a Dyson equation for the semiclassical Green's function we…
We show that for planar dispersing billiards the return times distribution is, in the limit, Poisson for metric balls almost everywhere w.r.t. the SRB measure. Since the Poincar\'e return map is piecewise smooth but becomes singular at the…
Using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents and the…
In this paper, we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model "diffusion-based" because its hamiltonian can be recovered from a simple dynamic procedure, which…