On a fundamental theorem in the theory of dispersing billiards

L. A. Bunimovič, Ja G. Sinaĭ

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

Billiards are considered within domains in the plane or on the twodimensional torus with the euclidian metric, where the boundaries of these domains are everywhere convex inward. It is shown that the flow {St} generated by such a billiard is a K-system. A fundamental place is here assigned to the proof of the theorem showing that transversal fibers for the flow {St} consist “on the whole” of sufficiently long regular segments. From this theorem follow assertions on the absolute continuity of transversal fibers for the billiards in question.

Original languageEnglish (US)
Pages (from-to)407-423
Number of pages17
JournalMathematics of the USSR - Sbornik
Volume19
Issue number3
DOIs
StatePublished - Apr 30 1973

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On a fundamental theorem in the theory of dispersing billiards'. Together they form a unique fingerprint.

  • Cite this