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 …

Mathematical billiards describe the motion of a mass point in a domain with elastic
reflections off the boundary or, equivalently, the behavior of rays of light in a domain with …

We prove some recent experimental observations of Dan Reznik concerning periodic billiard
orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon …

In this note we link symplectic and convex geometry by relating two seemingly different open
conjectures: a symplectic isoperimetric-type inequality for convex domains and Mahler's …

We consider several topological integrable billiards and prove that they are Liouville
equivalent to many systems of rigid body dynamics. The proof uses the Fomenko–Zieschang …

Рассмотрен ряд топологических интегрируемых биллиардов и доказана их лиувиллева
эквивалентность многим системам динамики твердого тела с помощью теории …

In this paper, we use the Ekeland–Hofer–Zehnder symplectic capacity to provide several
bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth …

In pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a
pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian …

This is an updated and expanded version of our earlier survey article [E. Gutkin,“Billiard
dynamics: a survey with the emphasis on open problems,” Regular Chaotic Dyn. 8, 1–13 …

Magnetic billiards in a convex domain with smooth boundary on a constant-curvature
surface in a constant magnetic field is considered in this paper. The question of the …