Nonperturbative aspects of the quantum chaos theory

A new approach to Quantum Chaos and certain related questions of Classical Dynamical theory are considered. We are interested in developing analytical methods, using the recently discovered Fried-Gabellini representation, which allow one to extend the properties of classical dynamics into the quantum area. This formalism is further developed in the context of quantum chaos theory. Using a nonperturbative approximation technique, a set of Trace Formulas is obtained outside the semiclassical limit. The nonperturbativity is particularly important for dealing with potentially chaotic systems and assures consistency of the approach. The effect of chaos suppression by the random fields of quantum radiative corrections is discussed in the limit, and a possible suppression mechanism is offered. Since the effect of chaos suppression by random signals has also been observed experimentally for low dimensional classical systems, a possible classical analog of the radiative chaos suppression mechanism is discussed, and a possible scenario of global stabilization of the periodic trajectories is presented. Unlike the other (mostly local) periodic orbit stabilization methods, this one is based on creating global phase space stability structures in the vicinity of a periodic orbit. Some results of certain numerical experiments are used for illustration purposes