Related papers: Billiards with Markovian reflection laws

We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting,…

Recent experiments and numerical simulations have shown that certain types of microorganisms "reflect" off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active…

We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…

We investigate statistical properties of several classes of periodic billiard models which are diffusive. An introductory chapter gives motivation, and then a review of statistical properties of dynamical systems is given in chapter 2. In…

A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are…

In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…

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.

In this paper, we show that billiard orbits in rational polygons and geodesics on translation surfaces exhibit super-fast spreading, an optimal time-quantitative majority property about the corresponding linear flow that implies uniformity…

Inspired by the work of Pujals and Sambarino on dominated splitting, we present billiards with a modified reflection law which constitute simple examples of dynamical systems with limit sets with dominated splitting and where the dynamics…

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…

In an ordinary billiard 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…

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…

We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated…

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…

Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds…

Given a random map (T_1, T_2, T_3, T_4, p_1, p_2, p_3, p_4), we define a random billiard map on a surface of constant curvature (Euclidean plane, hyperbolic plane, or the sphere). The Liouville measure is invariant for this billiard map.…

We study the motion of classical particles confined in a two-dimensional "nuclear" billiard whose walls undergo periodic shape oscillations according to a fixed multipolarity. The presence of a coupling term in the single particle…

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 the problem of arithmetic billiards from a new perspective. We first raise a similar problem about reflecting lights inside grids. For the solution to this problem, we will give three proofs. Next, we consider a similar problem in…

We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the…