Abstract
We study periodic orbits of the billiard ball map in a strictly convex domain with a C∞ boundary. We conjecture that the Lebesgue measure of all periodic points is 0. We are able to prove the following partial result: the measure of period three periodic orbits is 0. The question of whether the mentioned measure is 0 appeared in the study of spectral invariants of a planar region. The author learned about it from R. Melrose.
Original language | English (US) |
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Pages (from-to) | 191-205 |
Number of pages | 15 |
Journal | Journal of Differential Geometry |
Volume | 30 |
Issue number | 1 |
DOIs | |
State | Published - Jul 1989 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology