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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 $\partial D$, assume that the symplectic billiard map ha
Externí odkaz:
http://arxiv.org/abs/2402.19154
Autor:
Baracco, Luca, Bernardi, Olga
In this paper we prove that a totally integrable strictly-convex symplectic billiard table, whose boundary has everywhere strictly positive curvature, must be an ellipse. The proof, inspired by the analogous result of Bialy for Birkhoff billiards, us
Externí odkaz:
http://arxiv.org/abs/2305.19701
In this article we investigate rigidity properties of integrable area-preserving twist maps of the cylinder. More specifically, we prove that if a deformation of the standard integrable map preserves rotational invariant circles (i.e., homotopically
Externí odkaz:
http://arxiv.org/abs/2011.10997
Autor:
Kaloshin, Vadim, Sorrentino, Alfonso
Given a strictly convex domain $\Omega$ in $\R^2$, there is a natural way to define a billiard map in it: a rectilinear path hitting the boundary reflects so that the angle of reflection is equal to the angle of incidence. In this paper we answer a r
Externí odkaz:
http://arxiv.org/abs/1203.1274