Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse

Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. arXiv, 2111.12171.

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Abstract
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.
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Date Published
2021-11-23
Journal Title
arXiv
Article Number
2111.12171
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Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. arXiv. doi:10.48550/ARXIV.2111.12171
Koval, I. (n.d.). Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. arXiv. https://doi.org/10.48550/ARXIV.2111.12171
Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity of Almost Every Ellipse.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2111.12171.
I. Koval, “Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse,” arXiv. .
Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. arXiv, 2111.12171.
Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity of Almost Every Ellipse.” ArXiv, 2111.12171, doi:10.48550/ARXIV.2111.12171.
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