Related papers: Escape Rates and Physically Relevant Measures for …

We study the low energy quantum spectra of two-dimensional rectangular billiards with a small but finite-size scatterer inside. We start by examining the spectral properties of billiards with a single pointlike scatterer. The problem is…

The notion of a rough two-dimensional (convex) body is introduced, and to each rough body there is assigned a measure on $\TTT^3$ describing billiard scattering on the body. The main result is characterization of the set of measures…

Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls, have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi-)permeable walls…

For a class of non-uniformly hyperbolic interval maps, we study rates of escape with respect to conformal measures associated with a family of geometric potentials. We establish the existence of physically relevant conditionally invariant…

In the open circular billiard particles are placed initially with a uniform distribution in their positions inside a planar circular vesicle. They all have velocities of the same magnitude, whose initial directions are also uniformly…

We study billiard dynamics inside an ellipse for which the axes lengths are changed periodically in time and an $O(\delta)$-small quartic polynomial deformation is added to the boundary. In this situation the energy of the particle in the…

Since the seminal work of Sinai one studies chaotic properties of planar billiards tables. Among them is the study of decay of correlations for these tables. There are examples in the literature of tables with exponential and even…

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement…

We present a functional analytic framework based on the spectrum of the transfer operator to study billiard maps associated with perturbations of the periodic Lorentz gas. We show that recently constructed Banach spaces for the billiard map…

In this note we discuss limit distribution of normalized return times for shrinking targets and draw a necessary and sufficient condition using sweep-out sequence in order for the limit distribution to be exponential with parameter $1$. The…

We study the family of quadratic maps f_a(x) = 1 - ax^2 on the interval [-1,1] with a between 0 and 2. When small holes are introduced into the system, we prove the existence of an absolutely continuous conditionally invariant measure using…

Understanding the statistical properties of the aperiodic planar Lorentz gas stands as a grand challenge in the theory of dynamical systems. Here we study a greatly simplified but related model, proposed by Arvind Ayyer and popularized by…

We present an efficient method to solve scattering problems in two-dimensional open billiards with two leads and a complicated scattering region. The basic idea is to transform the scattering region to a rectangle, which will lead to…

We construct Birkhoff cones for dispersing billiards, which are contracted by the action of the transfer operator. This construction permits the study of statistical properties not only of regular dispersing billiards but also of sequential…

We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii…

We consider a billiard in the plane with periodic configuration of convex scatterers. This system is recurrent, in the sense that almost every orbit comes back arbitrarily close to the initial point. In this paper we study the time needed…

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary, and also a circular scatterer in the interior of the disk. We investigate stability properties of some…

We consider a strictly convex billiard table with $C^2$ boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation…

Given a domain or, more generally, a Riemannian manifold with boundary, a billiard is the motion of a particle when the field of force is absent. Trajectories of such a motion are geodesics inside the domain; and the particle reflects from…

We consider product of expansive Markov maps on an interval with hole which is conjugate to a subshift of finite type. For certain class of maps, it is known that the escape rate into a given hole does not just depend on its size but also…