This book covers one of the most exciting but most difficult topics in the modern theory of
dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical …

Publisher Summary The theory of mathematical billiards can be partitioned into three areas:
convex billiards with smooth boundaries, billiards in polygons (and polyhedra), and …

In this chapter we briefly give the theory (without proofs) of discrete and continuous-time
dynamical systems. This will be helpful for the reader, because a mathematical billiard which …

PERIODIC BILLIARD ORBITS ARE DENSE IN RATIONAL POLYGONS 1. Introduction A billiard
ball, ie a point mass, moves inside a polyg Page 1 TRANSACTIONS OF THE AMERICAN …

We examine the transport behaviour of non-interacting particles in a simple channel billiard,
at equilibrium and in the presence of an external field. We observe a range of sub-diffusive …

From extensive numerical simulations, we find that periodic polygonal billiard channels with
angles which are irrational multiples of π generically exhibit normal diffusion (linear growth …

We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also
knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard …

Billiard systems provide classic examples of simple mechanical systems. Among such
systems the simplest are those that model the motion of a single particle in a region P of the …

We investigate the onset of diffusive behavior in polygonal channels for disks of finite size,
modeling simple microporous membranes. It is well established that the point-particle case …

A billiard ball, ie a point mass, moves inside a polygon Q c JR2 with unit speed along a
straight line until it reaches the boundary 0Q, then instantaneously changes direction …