NONUNIFORM STATIONARY MEASURE PROPERTIES OF CHAOTIC AREA-PRESERVING DYNAMICAL-SYSTEMS

This article shows the existence of a non-uniform stationary measure ( referred to as the w-invariant measure) associated with the space-fill ing properties of the unstable manifold and characterizing some statis tical properties of chaotic two-dimensional area-preserving systems. T he w-invariant measure, which differs from the ergodic measure and is non-uniform in general, plays a central role in the statistical charac terization of chaotic fluid mixing systems, since several properties o f partially mixed structures can be expressed as ensemble averages ove r the w-invariant measure. A closed-form expression for the w-invarian t density is obtained for a class of mixing systems topologically conj ugate with the linear toral automorphism. The physical implications in the theory of fluid mixing, and in the statistical characterization o f chaotic Hamiltonian systems, are discussed. (C) 1998 Elsevier Scienc e B.V. All rights reserved.