эргодический тор

BIRTH OF A STABLE TORUS FROM THE CRITICAL CLOSED CURVE AND ITS BIFURCATIONS IN A LASER SYSTEM WITH FREQUENCY DETUNING

Realization of stable two­frequency oscillations is shown in the Maxwell–Bloch model. Birth of a stable ergodic two­dimensional torus from the critical closed curve is observed. The conditions of the passage to chaos via a cascade of torus doubling bifurcations are obtained. It is established that at bifurcations points a structurally unstable three­dimensional torus is produced, which gives rise to a stable doubled ergodic torus. Analytical approximation describing dynamics of the system near a point of torus birth is found.