相关论文: Billiards correlation functions

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…

We consider time-dependence of dynamical transport, following a recent study of the stadium billiard in which classical transmission and reflection probabilities were shown to exhibit exponential or algebraic decay depending on the choice…

Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick…

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are…

In an ordinary billiard system trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is…

Dynamical properties are studied for escaping particles, injected through a hole in an oval billiard. The dynamics is considered for both static and periodically moving boundaries. For the static boundary, two different decays for the…

We prove exponential correlation decay in dispersing billiard flows on the 2-torus assuming finite horizon and lack of corner points. With applications aimed at describing heat conduction, the highly singular initial measures are…

Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance with the laws of conservation of energy and momentum. For…

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…

We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional…

We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform…

We explore the dynamical evolution of an ensemble of non-interacting particles propagating freely in an elliptical billiard with harmonically driven boundaries. The existence of Fermi acceleration is shown thereby refuting the established…

We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…

The changeover from normal to super diffusion in time dependent billiards is explained analytically. The unlimited energy growth for an ensemble of bouncing particles in time dependent billiards is obtained by means of a two dimensional…

We investigate the transmission and reflection survival probabilities for the chaotic stadium billiard with two holes placed asymmetrically. Classically, these distributions are shown to have algebraic or exponential decays depending on the…

It is known that the dynamics of planar billiards satisfies strong mixing properties (e.g. exponential decay of correlations) provided that some expansion condition on unstable curves is satisfied. This condition has been shown to always…

We investigate the decay rates of correlations for nonuniformly hyperbolic systems with or without singularities, on piecewise H\"older observables. By constructing a new scheme of coupling methods using the probability renewal theory, we…

The present work consists of a numerical study of the dynamics of irrational polygonal billiards. Our contribution reinforces the hypothesis that these systems could be Strongly Mixing, although never demonstrably chaotic, and discuss the…

Rounding border effects at the escape point of open integrable billiards are analyzed via the escape times statistics and emission angles. The model is the rectangular billiard and the shape of the escape point is assumed to have a…

We study the collision dynamics of a spinning cue ball approaching a static object ball with equal mass on a plane, common in billiards. While typical collisions in billiards are nearly perfectly elastic, with a restitution coefficient…