Billiard Dynamics: An Updated Survey with the Emphasis on Open Problems

Abstract

This is an updated and expanded version of our earlier survey article \cite{Gut5}. Section $\S 1$ introduces the subject matter. Sections $\S 2-\S 4$ expose the basic material following the paradigm of elliptic, hyperbolic and parabolic billiard dynamics. In section $\S 5$ we report on the recent work pertaining to the problems and conjectures exposed in the survey \cite{Gut5}. Besides, in section $\S 5$ we formulate a few additional problems and conjectures. The bibliography has been updated and considerably expanded.

References in corpus (6)

• On triangular billiards
• Dynamics on an infinite surface with the lattice property
• On conjugacy of convex billiards
• Numerical exploration of a hexagonal string billiard
• A few remarks on periodic orbits for planar billiard tables
• Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane