Related papers: Statistical properties of type D dispersing billia…
The periodic wind-tree model is an infinite billiard in the plane with identical rectangular scatterers disposed at each integer point. We prove that independently of the size of the scatterers, generically with respect to the angle, the…
We study, analytically and numerically, the classical and quantum properties of a nearly spherical 3D billiard. In particular we show the appearence of quantum non ergodic behaviour and of the deviations from Random Matrix Theory…
We prove some partial results on the periodicity of billiard systems on graphs. The results specialize to the case of $n$ billiards with equal mass on the unit interval or circle traveling at the same speed.
We identify a collection of periodic billiard orbits in a self-similar Sierpinski carpet billiard table. Based on a refinement of the result of Durand-Cartagena and Tyson regarding nontrivial line segments in a self-similar Sierpinski…
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…
It is demonstrated numerically that smooth three degrees of freedom Hamiltonian systems which are arbitrarily close to three dimensional strictly dispersing billiards (Sinai billiards) have islands of effective stability, and hence are…
We consider billiard systems within compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We derive conditions for elliptic periodicity for such billiards. We describe the topology of those…
We consider two nested billiards in $\mathbb R^d$, $d\geq3$, with $C^2$-smooth strictly convex boundaries. We prove that if the corresponding actions by reflections on the space of oriented lines commute, then the billiards are confocal…
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 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…
The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motion of a point particle in this configuration space with…
Wire billiard is defined by a smooth embedded closed curve of non-vanishing curvature $k$ in $\mathbb{R}^n$ (a wire). For a class of curves, that we call nice wires, the wire billiard map is area preserving twist map of the cylinder. In…
We study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with double rotations and study orbit behavior and questions of complexity.
We study the convergence towards the equilibrium for a dissipative and stochastic time-dependent oval billiard. The dynamics of the system is described by using a generic four dimensional nonlinear map for the variables: the angular…
We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach…
This is the first survey of highly excited eigenstates of a chaotic 3D billiard. We introduce a strongly chaotic 3D billiard with a smooth boundary and we manage to calculate accurate eigenstates with sequential number (of a 48-fold…
The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and…
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods for reconstructing from the bounce spectrum of a polygonal…
For hyperbolic systems with singularities, such as dispersing billiards, Pesin theory as developed by Katok and Strelcyn applies to measures that are "adapted" in the sense that they do not give too much weight to neighborhoods of the…
We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…