This book explores infinite-type translation surfaces and is intended as an introductory text
for graduate and PhD students, as well as a reference for more advanced researchers …

This is an updated and expanded version of our earlier survey article [E. Gutkin,“Billiard
dynamics: a survey with the emphasis on open problems,” Regular Chaotic Dyn. 8, 1–13 …

We study stochastic billiards in infinite planar domains with curvilinear boundaries: that is,
piecewise deterministic motion with randomness introduced via random reflections at the …

Let be a sufficiently smooth convex function, vanishing at infinity. Consider the planar
domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f …

In a previous paper (Degli Esposti, Del Magno and Lenci 1998 An infinite step billiard
Nonlinearity 11 991-1013) we defined a class of non-compact polygonal billiards, the infinite …

We establish the background for the study of geodesics on noncompact polygonal surfaces.
For illustration, we study the recurrence of geodesics on ℤ-periodic polygonal surfaces. We …

We introduce billiards in polygons with an infinite number of sides. We show that for almost
every point the billiard flow in an infinite polygon is defined for all times and the Poincaré …

We consider the interaction between passing to finite covers and ergodic properties of the
straight-line flow on finite-area translation surfaces with infinite topological type. Infinite type …

Billiards are dynamical systems generated by the uniform linear motion of a point particle
inside a connected domain Q with unit speed and elastic reflections at the boundary∂ Q. A …

Abstract In [DDL] and [DDL2](in collaboration with G. Del Magno e M. Lenci) we defined a
class of non-compact polygonal billiards, the infinite step billiards: to a given sequence of …