Noncompact CPN as a phase space of superintegrable systems

Abstract

We propose the description of superintegrable models with dynamical [Formula: see text] symmetry, and of the generic superintegrable deformations of oscillator and Coulomb systems in terms of higher-dimensional Klein model (the noncompact analog of complex projective space) playing the role of phase space. We present the expressions of the constants of motion of these systems via Killing potentials defining the [Formula: see text] isometries of the Kähler structure.