Billiard Dynamics: An Updated Survey with the Emphasis on Open Problems
arXiv:1301.2547
Abstract
This is an updated and expanded version of our earlier survey article \cite{Gut5}. Section introduces the subject matter. Sections expose the basic material following the paradigm of elliptic, hyperbolic and parabolic billiard dynamics. In section we report on the recent work pertaining to the problems and conjectures exposed in the survey \cite{Gut5}. Besides, in section we formulate a few additional problems and conjectures. The bibliography has been updated and considerably expanded.
References in corpus (15)
- Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
- Mixing property of triangular billiards
- On triangular billiards
- Dynamics on an infinite surface with the lattice property
- Non-ergodic Z-periodic billiards and infinite translation surfaces
- Escape orbits and Ergodicity in Infinite Step Billiards
- Growth rates for geometric complexities and counting functions in polygonal billiards
- Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces
- Topological entropy and blocking cost for geodesics in riemannian manifolds
- Numerical exploration of a hexagonal string billiard
- On conjugacy of convex billiards
- A few remarks on periodic orbits for planar billiard tables
- Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane
- Real Analytic Metrics on S^2 with Total Absence of Finite Blocking
- Growth of periodic orbits and generalized diagonals for typical triangle billiards