The paper surveys open problems and questions related to different aspects of integrable
systems with finitely many degrees of freedom. Many of the open problems were suggested …

In this survey, we provide a concise introduction to convex billiards and describe some
recent results, obtained by the authors and collaborators, on the classification of integrable …

The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable
billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a …

In this paper we prove the Birkhoff-Poritsky conjecture for centrally-symmetric C^2-smooth
convex planar billiards. We assume that the domain A between the invariant curve of 4 …

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 …

We prove that equivalence classes of marked length isospectral Birkhoff billiard tables are
compact in C^ 2, analogous to the Laplace spectral results of Melrose and Osgood-Phillips …

In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196
(1): 389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally …

The aim of this work is to continue the analysis, started in arXiv: 2105.02108, of the
dynamics of a point-mass particle $ P $ moving in a galaxy with an harmonic biaxial core, in …

We consider a new type of dynamical systems of physical interest, where two different forces
act in two complementary regions of the space, namely a Keplerian attractive center sits in …

It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville
metrics. In this paper, we study a deformative version of this conjecture: we consider …