On the marked length spectrum of generic strictly convex billiard tables

Guan Huang; Vadim Kaloshin; Alfonso Sorrentino

doi:10.1215/00127094-2017-0038

Abstract

In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard map from the (maximal) marked length spectrum of the domain.

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Guan Huang. Vadim Kaloshin. Alfonso Sorrentino. "On the marked length spectrum of generic strictly convex billiard tables." Duke Math. J. 167 (1) 175 - 209, 15 January 2018. https://doi.org/10.1215/00127094-2017-0038

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Received: 17 June 2016; Revised: 23 June 2017; Published: 15 January 2018

First available in Project Euclid: 8 December 2017

zbMATH: 06847244

MathSciNet: MR3743701

Digital Object Identifier: 10.1215/00127094-2017-0038

Subjects:

Primary: 35P30

Secondary: 37D50 , 37E40 , 37J50

Keywords: action of periodic orbits , convex billiards , Laplace spectrum , marked length spectrum and length spectrum , Mather beta function

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