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- W4387560027 abstract "We prove that equivalence classes of marked length isospectral Birkhoff billiard tables are compact in C^2, analogous to the Laplace spectral results of Melrose and Osgood-Phillips-Sarnak. To do this, we use the first 5 Taylor coefficients of the mean minimal action, also called Mather's beta function. We also conjecture a hierarchical structure for the integral invariants of Marvizi-Melrose, or equivalently the coefficients of the caustic length-Lazutkin parameter expansion, which are in turn algebraically equivalent to those of Mather's beta function. Under the noncoincidence condition of Marvizi-Melrose, these are also Laplace spectral invariants and can be used to hear the shape of certain drumheads. A subsequent paper or an updated version of this one will address the structure of higher order invariants, which allows us to upgrade compactness to the smooth case." @default.
- W4387560027 created "2023-10-12" @default.
- W4387560027 creator A5034671839 @default.
- W4387560027 date "2023-10-09" @default.
- W4387560027 modified "2023-10-18" @default.
- W4387560027 title "Compactness of Marked Length Isospectral Sets of Birkhoff Billiard Tables" @default.
- W4387560027 doi "https://doi.org/10.48550/arxiv.2310.05426" @default.
- W4387560027 hasPublicationYear "2023" @default.
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