On July 9, 2001, Springer invited me to contribute a monograph on dynamical systems. I
immediately accepted, offering to write a book on dynamical zeta functions and dynamical …

The Lorentz gas, a point particle making mirror-like reflections from an extended collection of
scatterers, has been a useful model of deterministic diffusion and related statistical …

We give a review of results on superpolynomial decay of correlations, and polynomial decay
of correlations, for nonuniformly expanding semiflows and nonuniformly hyperbolic flows. A …

The Lorentz gas is a billiard model involving a point particle diffusing deterministically in a
periodic array of convex scatterers. In the two dimensional finite horizon case, in which all …

We prove a superdiffusive central limit theorem for the displacement of a test particle in the
periodic Lorentz gas in the limit of large times t and low scatterer densities (Boltzmann–Grad …

arxiv:2009.06284v2 [cond-mat.stat-mech] 1 Oct 2020 Page 1 WHAT MATHEMATICAL
BILLIARDS TEACH US ABOUT STATISTICAL PHYSICS? PÉTER BÁLINT, THOMAS GILBERT …

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

The Lorentz gas is one of the simplest, most widely used models to study the transport
properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting …

The theory of planar hyperbolic billiards is already quite well developed by having also
achieved spectacular successes. In addition there also exists an excellent monograph by …

We consider the motion of two point masses along a vertical half-line that are subject to
constant gravitational force and collide elastically with each other and the floor. This model …