Dynamical systems with elastic reflections

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Abstract

In this paper we consider dynamical systems resulting from the motion of a material point in domains with strictly convex boundary, that is, such that the operator of the second quadratic form is negative-definite at each point of the boundary, where the boundary is taken to be equipped with the field of inward normals. We prove that such systems are ergodic and are -systems. The basic method of investigation is the construction of transversal foliations for such systems and the study of their properties.

Original languageEnglish (US)
Pages (from-to)137-189
Number of pages53
JournalRussian Mathematical Surveys
Volume25
Issue number2
DOIs
StatePublished - Apr 30 1970

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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