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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 |
| Appears in Collections: | Journal Articles |
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