Numerical evidence of Dynamical spectral rigidity of ellipses among smooth $\mathbb{Z}_2$-symmetric domains

TL;DR

This paper provides numerical evidence supporting the spectral rigidity of $ ext{Z}_2$-symmetric elliptical domains with eccentricity less than 0.30, indicating their spectral properties are uniquely determined by their shape.

Contribution

The study offers the first numerical validation of spectral rigidity for a class of symmetric elliptical domains, expanding understanding of inverse spectral problems.

Findings

Spectral rigidity observed numerically for ellipses with eccentricity < 0.30

Evidence suggests shape is uniquely determined by spectral data within this class

Supports conjecture of spectral uniqueness for symmetric elliptical domains

Abstract

We present numerical evidence for spectral rigidity among $\mathbb{Z}_{2}$-symmetric domains of ellipses of eccentricity smaller than $0.30$.