Bounds for Minkowski Billiard trajectories in convex bodies

Shiri Artstein-Avidan; Yaron Ostrover

doi:10.1093/imrn/rns216

Bounds for Minkowski Billiard trajectories in convex bodies

Shiri Artstein-Avidan, Yaron Ostrover

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we use the Ekeland-Hofer-Zehnder symplectic capacity to provide several bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth convex body in Rⁿ. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiards.

Original language	English
Pages (from-to)	165-193
Number of pages	29
Journal	International Mathematics Research Notices
Volume	2014
Issue number	1
DOIs	https://doi.org/10.1093/imrn/rns216
State	Published - 1 Jan 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rns216

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author = "Shiri Artstein-Avidan and Yaron Ostrover",

note = "Funding Information: This article was partially supported by ISF grant No. 247/11 (to S.A.-A.) and by a Reintegration Grant SSGHD-268274 within the 7th European community framework programme, and by the ISF grant No. 1057/10 (to Y.O.) and also by BSF grant number 2006079 (to S.A.-A. and Y.O.).",

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Bounds for Minkowski Billiard trajectories in convex bodies

Abstract

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