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 …

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 …

In this article we introduce a simple dynamical system called symplectic billiards. As
opposed to usual/Birkhoff billiards, where length is the generating function, for symplectic …

In a study of capillary floating, Finn (J Math Fluid Mech 11: 443–458, 2009) described a
procedure for determining cross-sections of non-circular, infinite convex cylinders that float …

Ivrii's Conjecture states that in every billiard in Euclidean space the set of periodic orbits has
measure zero. It implies that for every k≥ 2there are no k-reflective billiards, ie, billiards …

A caustic of a billiard table is a curve such that any billiard trajectory, once tangent to the
curve, stays tangent after every reflection at the boundary. When the billiard table is an …

Wire billiard is defined by a smooth embedded closed curve of non-vanishing curvature k in
R n (a wire). For a class of curves, that we call nice wires, the wire billiard map is area …

We show that in the space of all convex billiard boundaries, the set of boundaries with
rational caustics is dense. More precisely, the set of billiard boundaries with caustics of …

Following a recent paper by Baryshnikov and Zharnitskii, we consider outer billiards in the
plane possessing invariant curves consisting of periodic orbits. We prove the existence and …

Self-dual polygons and self-dual curves Page 1 FAOM Funct. Anal. Other Math. (2009) 2:
203–220 DOI 10.1007/s11853-008-0020-5 Self-dual polygons and self-dual curves Dmitry …