Quantum Chaos in Mixed Phase Space and the Julia Set

Abstract

Recent studies on complex dynamical systems in more than one dimension have revealed that even if the real phase space is a mixture of KAM tori and chaotic seas there exists a unique ergodic measure in the complex phase space which is (weakly) hyperbolic and gives maximal entropy of the dynamics. We present several pieces of numerical evidence and speculations on the existence of rotational domains in the complex space, implying that the measure thus obtained satisfies desired properties of the support of semiclassical wavefunctions in the mixed phase space.