PreprintarXiv licencearXiv
Infinitesimal dynamical spectral rigidity of the Bunimovich stadium
Abstract
We prove the infinitesimal dynamical spectral rigidity of the circular Bunimovich stadium with sufficiently long flat edges, in the class of domains obtained by replacing its two circular arcs with strictly convex C4 arcs and keeping its reflection symmetry across the axis parallel to the flat edges. That is, if a C1 one-parameter family in this class passing through the stadium preserves the length spectrum, then its deformation function at the stadium vanishes identically. For flat edges of arbitrary length, the deformation functions of such families still span a finite-dimensional space.
Related
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BibTeX
@misc{shi2026infinitesimal,
title = {{Infinitesimal dynamical spectral rigidity of the Bunimovich stadium}},
author = {Xianghui Shi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16241},
eprint = {2609.16241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16241},
}
RIS
TY - UNPB
TI - Infinitesimal dynamical spectral rigidity of the Bunimovich stadium
AU - Xianghui Shi
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16241
UR - https://arxiv.org/abs/2609.16241
AB - We prove the infinitesimal dynamical spectral rigidity of the circular Bunimovich stadium with sufficiently long flat edges, in the class of domains obtained by replacing its two circular arcs with strictly convex C^4 arcs and keeping its reflection symmetry across the axis parallel to the flat edges. That is, if a C^1 one-parameter family in this class passing through the stadium preserves the length spectrum, then its deformation function at the stadium vanishes identically. For flat edges of arbitrary length, the deformation functions of such families still span a finite-dimensional space.
ER -