# Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle

De Simoi J, Kaloshin V, Wei Q. 2017. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. Annals of Mathematics. 186(1), 277–314.

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Author

De Simoi, Jacopo;
Kaloshin, Vadim

^{IST Austria}^{}; Wei, QiaolingAbstract

We show that any sufficiently (finitely) smooth ℤ₂-symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all deformations among domains in the same class that preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak.

Publishing Year

Date Published

2017-07-01

Journal Title

Annals of Mathematics

Volume

186

Issue

1

Page

277-314

ISSN

IST-REx-ID

### Cite this

De Simoi J, Kaloshin V, Wei Q. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle.

*Annals of Mathematics*. 2017;186(1):277-314. doi:10.4007/annals.2017.186.1.7De Simoi, J., Kaloshin, V., & Wei, Q. (2017). Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle.

*Annals of Mathematics*. Annals of Mathematics. https://doi.org/10.4007/annals.2017.186.1.7De Simoi, Jacopo, Vadim Kaloshin, and Qiaoling Wei. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.”

*Annals of Mathematics*. Annals of Mathematics, 2017. https://doi.org/10.4007/annals.2017.186.1.7.J. De Simoi, V. Kaloshin, and Q. Wei, “Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle,”

*Annals of Mathematics*, vol. 186, no. 1. Annals of Mathematics, pp. 277–314, 2017.De Simoi, Jacopo, et al. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.”

*Annals of Mathematics*, vol. 186, no. 1, Annals of Mathematics, 2017, pp. 277–314, doi:10.4007/annals.2017.186.1.7.**All files available under the following license(s):**

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arXiv 1606.00230