Topological entropy of semi-dispersing billiards
1998 ◽
Vol 18
(4)
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pp. 791-805
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Keyword(s):
In this paper we continue to explore the applications of the connections between singular Riemannian geometry and billiard systems that were first used in [6] to prove estimates on the number of collisions in non-degenerate semi-dispersing billiards.In this paper we show that the topological entropy of a compact non-degenerate semi-dispersing billiard on any manifold of non-positive sectional curvature is finite. Also, we prove exponential estimates on the number of periodic points (for the first return map to the boundary of a simple-connected billiard table) and the number of periodic trajectories (for the billiard flow). In \S5 we prove some estimates for the topological entropy of Lorentz gas.
1998 ◽
Vol 18
(2)
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pp. 303-319
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2010 ◽
Vol 31
(1)
◽
pp. 49-75
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1995 ◽
Vol 05
(05)
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pp. 1351-1355
Keyword(s):
1991 ◽
Vol 33
(2)
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pp. 465-486
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2002 ◽
Vol 74
(4)
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pp. 589-597
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2018 ◽
Vol 2020
(5)
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pp. 1346-1365
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1998 ◽
Vol 49
(1)
◽
pp. 203-204
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