Bialy-Mironov type rigidity for centrally symmetric symplectic billiards
Year: 2024
Type: article
Abstract: The aim of the present paper is to establish a Bialy–Mironov type rigidity for centrally symmetric symplectic billiards. For a centrally symmetric C 2 strongly-convex domain D with boundary ∂ D , assume that the symplectic billiard map has a (simple) continuous invariant curve δ ⊂ P of rotation number 1 / 4 (winding once around ∂ D ) and consisting only of 4-periodic orbits. If one of the parts between δ and each boundary of the phase-space is entirely foliated by continuous invariant closed (not null-homotopic) curves, then ∂ D is an ellipse. The differences with Birkhoff billiards are essentially two: it is possible to assume the existence of the foliation in one of the parts of the phase-space detected by the curve δ, and the result is obtained by tracing back the problem directly to the totally integrable case.
Source: Nonlinearity
Authors: Luca Baracco, Olga Bernardi, Alessandra Nardi
Institution: University of Padua
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,165
OpenAlex ID: W4404340331