Bounds for Minkowski Billiard Trajectories in Convex Bodies

2011/11/09 by Shiri Artstein-Avidan, Artstein-Avidan, Shiri, Yaron Ostrover +1 · 1 citation
Mathematics · #52A20 #52A40 #53D35 #57R17 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:52A20 #msc:52A40 #msc:53D35 #msc:57R17

paper · pdf · doi:10.48550/arxiv.1111.2353

Latex, 26 pages

arxiv created 2012/08/30 · arxiv updated 2012/08/31

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 \mathbb Rⁿ. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiards.

Cited by

• Dynamical extensions of Zoll to nonsmooth convex bodies

Related

• Shortest Minkowski billiard trajectories on convex bodies
• Shortest closed billiard orbits on convex tables
• Minimizing length of billiard trajectories in hyperbolic polygons
• Periodic trajectories in 3-dimensional convex billiards
• Topology of billiard problems, II