Numerical Evidence of Robust Dynamical Spectral Rigidity of Ellipses Among Smooth -Symmetric Domains

DOI10.1080/10586458.2021.1980456arXiv2006.06042OpenAlexW3205536009MaRDI QIDQ6050734

Jacopo De Simoi, Unnamed Author

Publication date: 19 September 2023

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.06042

zbMATH Keywords

inverse problemlength spectrumconvex billiardsellipsesspectral rigidity

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Isospectrality (58J53) Dynamical systems with singularities (billiards, etc.) (37C83) Computational methods for invariant manifolds of dynamical systems (37M21) Equivariant dynamical systems (37C81)

Cites Work

• An integrable deformation of an ellipse of small eccentricity is an ellipse
• An inverse spectral result for elliptical regions of \(\mathbb{R}^2\)
• Spectral invariants of convex planar regions
• The propagation of singularities along gliding rays
• On the local Birkhoff conjecture for convex billiards
• One can hear the shape of ellipses of small eccentricity
• Dynamical spectral rigidity among \(\mathbb{Z}_2\)-symmetric strictly convex domains close to a circle
• Inverse spectral problem for analytic domains. II: \(\mathbb Z_2\)-symmetric domains
• One cannot hear the shape of a drum
• Can One Hear the Shape of a Drum?

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