Collisions in semi-dispersing billiard on Riemannian manifold
type: Item
instance of: scholarly article
title: Collisions in semi-dispersing billiard on Riemannian manifold
zbMATH Open document ID: 1079.37028
DOI: 10.1016/S0166-8641(01)00133-X
author: A. Kononenko
author: Dmitri Burago
author: S. Ferleger
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: The authors prove first for semidispersing billiards on arbitrary manifolds any trajectory makes only a finite number of collisions during a finite period of time. Then they establish local uniform estimates on the number of collisions for such billiards under a mild nondegeneracy condition. Moreover, the authors give effective estimates on the maximal number of collisions and the size of the neighborhood in which they may occur in terms of the nondegeneracy constant and some geometric properties of the manifold.
Mathematics Subject Classification ID: 37D50
Mathematics Subject Classification ID: 37A60
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 1787552
zbMATH Keywords: semidispersing billiard
zbMATH Keywords: nondegeneracy
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: number of collisions
Wikidata QID: Q115339631
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787552