We explain and justify that the only mechanisms of chaotic dynamics for billiards are
dispersing and defocusing. We also introduce boomerang billiards which dynamics …

We demonstrate that the defocusing mechanism fails to work if not all focusing components
of the boundary are absolutely focusing. More precisely, we construct billiard tables with …

We study a class of planar billiards having the remarkable property that their phase space
consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite …

We study, by numerical simulations and semi-rigorous arguments, a two-parameter family of
convex, two-dimensional billiard tables, generalizing the one-parameter class of oval …

We consider billiards in non-polygonal domains of the plane with boundary consisting of
curves of three different types: straight segments, strictly convex inward curves and strictly …

We consider extensions of non-singular maps which are exact, respectively K-mixing, or at
least have a decomposition into positive-measure exact, respectively K-mixing, components …

BILLIARDS AND STATISTICAL MECHANICS Page 1 BILLIARDS AND STATISTICAL
MECHANICS A Thesis Presented to The Academic Faculty by Alexander Grigo In Partial …

Many planar hyperbolic billiards are conjectured to be ergodic. This paper represents a first
step towards the proof of this conjecture. The Hopf argument is a standard technique for …

Smooth maps with singularities describe important physical phenomena such as the
collisions of rigid spheres among them and/or with the walls of a container. Questions about …

We prove that hyperbolic billiards constructed by Bussolari and Lenci are Bernoulli systems.
These billiards cannot be studied by existing approaches to analysis of billiards that have …