This article reviews the role of hidden symmetries of dynamics in the study of physical
systems, from the basic concepts of symmetries in phase space to the forefront of current …

A superintegrable system is a system that is integrable in the sense of Liouville–Arnold and
that, in addition to this, possesses more globally defined constants of motion than degrees of …

We study the properties of the symplectic sp (2N) algebra deformed by means of the Dunkl
operators, which describe the dynamical symmetry of the generalized N-particle Calogero …

arXiv:hep-th/9810176v1 22 Oct 1998 Page 1 arXiv:hep-th/9810176v1 22 Oct 1998 On the
equivalence of the rational Calogero–Moser system to free particles Tomasz Brzezinski 1 …

We construct the Runge-Lenz vector and the symmetry algebra of the rational Calogero-
Coulomb problem using the Dunkl operators. We reveal that they are proper deformations of …

We present a general scheme for constructing the Poisson structure of super-integrable
dynamical systems of which the rational Calogero–Moser system is the most interesting one …

We introduce the Dunkl version of the Laplace–Runge–Lenz vector associated with a finite
Coxeter group W acting geometrically in RN and with a multiplicity function g. This vector …

A bstract We investigate how the Lax-Novikov integral in the perfectly invisible PT-
regularized zero-gap quantum conformal and superconformal mechanics systems affects on …

We review the classical properties of Tremblay–Turbiner–Winternitz and Post–Wintenitz
systems and their relation with N-dimensional rational Calogero model with oscillator and …

We investigate the integrals of motion of general conformal mechanical systems with and
without confining harmonic potential as well as of the related angular subsystems, by …