One can hear the shape of ellipses of small eccentricity
H Hezari, S Zelditch - Annals of Mathematics, 2022 - projecteuclid.org
We show that if the eccentricity of an ellipse is sufficiently small, then up to isometries it is
spectrally unique among all smooth domains. We do not assume any symmetry, convexity …
spectrally unique among all smooth domains. We do not assume any symmetry, convexity …
On the persistence of periodic tori for symplectic twist maps and the rigidity of integrable twist maps
In this article we study the persistence of Lagrangian periodic tori for symplectic twist maps
of the $2 d $-dimensional annulus and prove a rigidity result for completely integrable ones …
of the $2 d $-dimensional annulus and prove a rigidity result for completely integrable ones …
Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture
P Corvaja, U Zannier - Proceedings of the London …, 2023 - Wiley Online Library
We offer some theorems, mainly finiteness results, for certain patterns in elliptical billiards,
related to periodic trajectories; these seem to be the first finiteness results in this context. For …
related to periodic trajectories; these seem to be the first finiteness results in this context. For …
[HTML][HTML] On the fragility of periodic tori for families of symplectic twist maps
In this article we study the fragility of Lagrangian periodic tori for symplectic twist maps of the
2d-dimensional annulus and prove a rigidity result for completely integrable ones. More …
2d-dimensional annulus and prove a rigidity result for completely integrable ones. More …
Periodic orbits for square and rectangular billiards
HH Chen, HM Osinga - arXiv preprint arXiv:2410.18316, 2024 - arxiv.org
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in
a straight line on a (perfectly friction-less) table, striking the sides according to the law of …
a straight line on a (perfectly friction-less) table, striking the sides according to the law of …
Inverse scattering via travelling times in billiards on manifolds
T Gurfinkel - 2024 - research-repository.uwa.edu.au
We present the first rigidity results for the Travelling Times Spectrum on Riemannian
manifolds for disjoint unions of strictly convex obstacles. Specifically, we show that under …
manifolds for disjoint unions of strictly convex obstacles. Specifically, we show that under …