---
_id: '14278'
abstract:
- lang: eng
  text: 'The Birkhoff conjecture says that the boundary of a strictly convex integrable
    billiard table is necessarily an ellipse. In this article, we consider a stronger
    notion of integrability, namely, integrability close to the boundary, and prove
    a local version of this conjecture: a small perturbation of almost every ellipse
    that preserves integrability near the boundary, is itself an ellipse. We apply
    this result to study local spectral rigidity of ellipses using the connection
    between the wave trace of the Laplacian and the dynamics near the boundary and
    establish rigidity for almost all of them.'
article_number: '2111.12171'
article_processing_charge: No
arxiv: 1
author:
- first_name: Illya
  full_name: Koval, Illya
  id: 2eed1f3b-896a-11ed-bdf8-93c7c4bf159e
  last_name: Koval
citation:
  ama: Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost
    every ellipse. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/ARXIV.2111.12171">10.48550/ARXIV.2111.12171</a>
  apa: Koval, I. (n.d.). Local strong Birkhoff conjecture and local spectral rigidity
    of almost every ellipse. <i>arXiv</i>. <a href="https://doi.org/10.48550/ARXIV.2111.12171">https://doi.org/10.48550/ARXIV.2111.12171</a>
  chicago: Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity
    of Almost Every Ellipse.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/ARXIV.2111.12171">https://doi.org/10.48550/ARXIV.2111.12171</a>.
  ieee: I. Koval, “Local strong Birkhoff conjecture and local spectral rigidity of
    almost every ellipse,” <i>arXiv</i>. .
  ista: Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost
    every ellipse. arXiv, 2111.12171.
  mla: Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity
    of Almost Every Ellipse.” <i>ArXiv</i>, 2111.12171, doi:<a href="https://doi.org/10.48550/ARXIV.2111.12171">10.48550/ARXIV.2111.12171</a>.
  short: I. Koval, ArXiv (n.d.).
date_created: 2023-09-06T08:35:43Z
date_published: 2021-11-23T00:00:00Z
date_updated: 2023-09-15T06:44:00Z
day: '23'
department:
- _id: GradSch
doi: 10.48550/ARXIV.2111.12171
external_id:
  arxiv:
  - '2111.12171'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2111.12171
month: '11'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Local strong Birkhoff conjecture and local spectral rigidity of almost every
  ellipse
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...