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Mat. Sb., 1991, Volume 182, Number 2, Pages 220–235 (Mi msb1293)  

This article is cited in 1 scientific paper (total in 1 paper)

On the behavior of trajectories of scattering billiards on the flat torus

I. K. Babenko


Abstract: Properties of trajectories of scattering billiards on the flat two-dimensional torus are considered. A Riemann surface is associated with such a billiard in a natural way, while the billiard flow lifts in a natural way to the manifold of linear elements of this Riemann surface. The lift of the billiard flow is a multivalued flow. The trajectories of the billiard flow are lifted from the Riemann surface to the Lobachevsky plane, and properties of the “exponential billiard mapping” are studied. On the absolute circle of the Lobachevsky plane there arise Cantor sets – “reachable sets” of the billiard flow. The metric characteristics – the Hausdorff dimension and the Pontryagin–Schnirelmann orders – of these Cantor sets are invariants of the original billiard system. The topological entropy of the billiard flow on the Riemann surface is estimated in terms of these invariants.

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English version:
Mathematics of the USSR-Sbornik, 1992, 72:1, 207–220

Bibliographic databases:

UDC: 517.938.5
MSC: 58F25, 58F11
Received: 29.03.1990

Citation: I. K. Babenko, “On the behavior of trajectories of scattering billiards on the flat torus”, Mat. Sb., 182:2 (1991), 220–235; Math. USSR-Sb., 72:1 (1992), 207–220

Citation in format AMSBIB
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\by I.~K.~Babenko
\paper On the behavior of trajectories of scattering billiards on the flat torus
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 2
\pages 220--235
\mathnet{http://mi.mathnet.ru/msb1293}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1103273}
\zmath{https://zbmath.org/?q=an:0776.58031|0724.58055}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..72..207B}
\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 1
\pages 207--220
\crossref{https://doi.org/10.1070/SM1992v072n01ABEH001268}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JF72300012}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. A. Gal'perin, “Asymptotic behaviour of a particle in a Lorentz gas”, Russian Math. Surveys, 47:1 (1992), 258–259  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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