Moscow Mathematical Journal

Volume 19, Issue 2, April–June 2019 pp. 307–327.

On the Finite Dimensionality of Integrable Deformations of Strictly Convex Integrable Billiard Tables

Authors: Guan Huang (1) and Vadim Kaloshin (2)
Author institution:(1) Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
(2) Department of Mathematics, University of Maryland, College Park, MD, USA

Summary:

In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table Ω₀ preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through Ω₀.

2010 Math. Subj. Class. 37E40, 37E45, 28D10.

Keywords: Convex billiards, integrable billiards, caustics.

Contents Full-Text PDF