Duke Mathematical Journal

On the marked length spectrum of generic strictly convex billiard tables

Guan Huang, Vadim Kaloshin, and Alfonso Sorrentino

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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.

Article information

Source
Duke Math. J., Volume 167, Number 1 (2018), 175-209.

Dates
Received: 17 June 2016
Revised: 23 June 2017
First available in Project Euclid: 8 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1512702098

Digital Object Identifier
doi:10.1215/00127094-2017-0038

Mathematical Reviews number (MathSciNet)
MR3743701

Zentralblatt MATH identifier
06847244

Subjects
Primary: 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory
Secondary: 37D50: Hyperbolic systems with singularities (billiards, etc.) 37E40: Twist maps 37J50: Action-minimizing orbits and measures

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

Citation

Huang, Guan; Kaloshin, Vadim; Sorrentino, Alfonso. On the marked length spectrum of generic strictly convex billiard tables. Duke Math. J. 167 (2018), no. 1, 175--209. doi:10.1215/00127094-2017-0038. https://projecteuclid.org/euclid.dmj/1512702098


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