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Title: Symplectic capacity and short periodic billiard trajectory
Authors: Irie, Kei
Author's alias: 入江, 慶
Keywords: Symplectic capacity
Periodic billiard trajectory
Symplectic homology
Issue Date: Dec-2012
Publisher: Springer-Verlag
Journal title: Mathematische Zeitschrift
Volume: 272
Issue: 3-4
Start page: 1291
End page: 1320
DOI: 10.1007/s00209-012-0987-y
Abstract: We prove that a bounded domain Ω in R^n with smooth boundary has a periodic billiard trajectory with at most n + 1 bounce times and of length less than C n r(Ω), where C n is a positive constant which depends only on n, and r(Ω) is the supremum of radius of balls in Ω. This result improves the result by C. Viterbo, which asserts that Ω has a periodic billiard trajectory of length less than C′nvol(Ω)^[1/n] . To prove this result, we study symplectic capacity of Liouville domains, which is defined via symplectic homology.
Rights: The final publication is available at www.springerlink.com
URI: http://hdl.handle.net/2433/162900
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