Dynamical spectral rigidity among \(\mathbb{Z}_2\)-symmetric strictly convex domains close to a circle. (English) Zbl 1377.37062

The main result of the paper states that any strictly convex domain sufficiently close to a circle, with sufficiently smooth boundary and axial symmetry is dynamically spectrally rigid, i.e., any \(C^1\)-smooth one-parameter dynamically isospectral family is isometric. The paper is densely written. With patience one can get from the proof all needed details and techniques. Moreover, the multilayered story of the problem in question is duly considered.


37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
35P05 General topics in linear spectral theory for PDEs
58J53 Isospectrality
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Full Text: DOI arXiv


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