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 …

Integrable Hamiltonian systems have been of growing interest over the past 30 years and
represent one of the most intriguing and mysterious classes of dynamical systems. This book …

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 …

We introduce an appropriate formalism in order to study conformal Killing (symmetric)
tensors on Riemannian manifolds. We reprove in a simple way some known results in the …

Here we consider the anharmonic oscillator that is a dynamical system given by yx x+ δ yn=
0. We demonstrate that to this equation corresponds a new example of a superintegrable …

The paper surveys open problems and questions related to geodesics defined by
Riemannian, Finsler, semi-Riemannian and magnetic structures on manifolds. It is an …

In the paper, a new class of integrable billiards, namely, billiards with slip**, is studied. At
the reflection from the boundary, a billiard particle of such a system may not only change its …

We suggest a construction that, given an orbital diffeomorphism between two Hamiltonian
systems, produces integrals of them. We treat geodesic equivalence of metrics as the main …

We discuss whether it is possible to reconstruct a metric from its nonparameterized
geodesics, and how to do it effectively. We explain why this problem is interesting for …

It is well known that the system of ordinary differential equations (ODEs) describing geodesic
flows of some Riemannian metrics on 2-surfaces admits a projection on a special class of …