Introduction to models on constant negative curvature surfaces
E. Bogomolny · 2020
Standard courses of classical and quantum mechanics often start with a lot of examples of systems which admit exact solutions. Harmonic oscillators, particles in Coulomb fields and other simple models are building stones of everyone&s;s knowledge. In classical mechanics the existence of chaotic trajectories has been known from the time of Poincaré and the theory of classical chaos is now one of the main parts of modern theory of dynamical systems. Much less is known about how classical chaotic motion manifests itself on quantum properties. The answer to this question is the main problem of the new and quickly growing domain of mathematical physics which had conditionally named ‘Quantum Chaos’. This name is attributed to investigations of deterministic quantum systems whose classical limit has certain chaotic properties. The important property of the plane is the existence of a 3-parameter group of isometric transformations.