On the Marked Length Spectrums of Generic Strictly Convex Billiard Tables

TL;DR

This paper demonstrates that for most strictly convex shapes, the spectral data related to special periodic orbits can be reconstructed from the domain's marked length spectrum, advancing inverse spectral geometry.

Contribution

It establishes a method to recover Aubry-Mather periodic orbit data from the marked length spectrum for generic strictly convex billiard tables.

Findings

Recovery of eigendata from length spectrum

Applicability to generic strictly convex domains

Advancement in inverse spectral problems

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.