Year: 2026
Type: preprint
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 $C^{4}$ 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.
Source: arXiv (Cornell University)
Author: Shi, Xianghui
Institution: University of California, Los Angeles
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213420067