On quadrilateral orbits in complex algebraic planar billiards
Dynamical Systems
2014-01-28 v2 Algebraic Geometry
Abstract
The famous conjecture of V.Ya.Ivrii (1978) says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study the complex algebraic version of Ivrii's conjecture for quadrilateral orbits in two dimensions, with reflections from complex algebraic curves. We present the complete classification of 4-reflective algebraic counterexamples: billiards formed by four complex algebraic curves in the projective plane that have open set of quadrilateral orbits.
Cite
@article{arxiv.1309.1843,
title = {On quadrilateral orbits in complex algebraic planar billiards},
author = {Alexey Glutsyuk},
journal= {arXiv preprint arXiv:1309.1843},
year = {2014}
}
Comments
64 pages. To appear in Moscow Math. Journal, No 2 (2014)