Billiards and nonholonomic distributions

Y. Baryshnikov, V. Zharnitsky

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this note, we consider billiards with full families of periodic orbits. It is shown that the construction of a convex billiard with a "rational" caustic (i.e., carrying only periodic orbits) can be reformulated as a problem of finding a closed curve tangent to an (N - 1)-dimensional distribution on a (2N - 1)-dimensional manifold. We describe the properties of this distribution, as well as some important consequences for billiards with rational caustics. A very particular application of our construction states that an ellipse can be infinitesimally perturbed so that any chosen rational elliptic caustic will persist.

Original languageEnglish
Pages (from-to)2706-2710
Number of pages5
JournalJournal of Mathematical Sciences
Volume128
Issue number2
DOIs
Publication statusPublished - Jul 1 2005
Externally publishedYes

Fingerprint

Caustic
Nonholonomic
Billiards
Orbits
Periodic Orbits
Closed curve
Ellipse
Tangent line

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

Cite this

Billiards and nonholonomic distributions. / Baryshnikov, Y.; Zharnitsky, V.

In: Journal of Mathematical Sciences, Vol. 128, No. 2, 01.07.2005, p. 2706-2710.

Research output: Contribution to journalArticle

Baryshnikov, Y. ; Zharnitsky, V. / Billiards and nonholonomic distributions. In: Journal of Mathematical Sciences. 2005 ; Vol. 128, No. 2. pp. 2706-2710.
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