The paper "Problems
on billiards, flat
surfaces and translation surfaces
" is published in
on Mapping Class Groups and Related Topics
", edited by
Proc. Symp. Pure Math., Amer. Math. Soc., 233-243, 2006
(see also the web-page of Benson Farb
the Editor, for the online version of the entire collection).
Several related problems can be found in the last paragraph of the long
survey A.Zorich, Flat
, in collection "Frontiers in Number Theory, Physics and
On random matrices, zeta functions and dynamical systems, P.
Cartier; B. Julia; P. Moussa; P. Vanhove (Editors),
Springer-Verlag, Berlin, 2006, 439-586.
Progress since the
paper was published
: In particular case,
when a flat surface is a tetrahedron
(a sphere with four conical points) closed geodesics are studied
V.Yu. Protassov, Closed geodesics on
the surface of a symplex
Sb.Mathematics (Matematicheskii Sbornik), 198
(2007), No 2, 103-121
. First results are
obtained in the paper: M.Kontsevich, Lyapunov exponents
, "The mathematical beauty of physics" (Saclay,
1996), (in Honor of C. Itzykson) 318-332, Adv.
Math. Phys., 24.
World Sci. Publishing, River Edge, NJ (1997) (see also arXiv).
Some results for Veech surfaces are obtained
in the paper:
Irene I. Bouw, Martin Moeller, Teichmueller
curves, triangle groups, and Lyapunov exponents
Genus 2 is studied in the paper:
Matt Bainbridge Euler
characteristics of Teichmüller curves in genus two
. Some interesting examples are constructed in the
J. Smillie, B. Weiss, Veech
dichotomy and the lattice property
2006; and in
Yitwah Cheung, Pascal Hubert , Howard Masur, Topological dichotomy and strict
ergodicity for translation surfaces