Geodesic
Dynamical spectral rigidity among $\mathbb{Z}_2$-symmetric strictly convex domains close to a circle (Appendix B coauthored with H. Hezari)
Jacopo De Simoi1 ; Vadim Kaloshin2 ; Qiaoling Wei3
1 University of Toronto, Toronto, ON, Canada
2 University of Maryland, College Park, MD
3 Capital Normal University, Beijing, PR China
Annals of mathematics, Tome 186 (2017) no. 1, pp. 277-314 Cet article a éte moissonné depuis la source Annals of Mathematics website

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We show that any sufficiently (finitely) smooth $\mathbb{Z}_2$-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.

DOI : 10.4007/annals.2017.186.1.7

Jacopo De Simoi 1 ; Vadim Kaloshin 2 ; Qiaoling Wei 3

1 University of Toronto, Toronto, ON, Canada
2 University of Maryland, College Park, MD
3 Capital Normal University, Beijing, PR China 
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Jacopo De Simoi; Vadim Kaloshin; Qiaoling Wei. Dynamical spectral rigidity among $\mathbb{Z}_2$-symmetric strictly convex domains  close to a circle (Appendix B coauthored with H. Hezari). Annals of mathematics, Tome 186 (2017) no. 1, pp. 277-314. doi: 10.4007/annals.2017.186.1.7

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