NONUNIFORM STATIONARY MEASURE OF THE INVARIANT UNSTABLE FOLIATION IN HAMILTONIAN AND FLUID MIXING SYSTEMS

This article demonstrates the existence of a nonuniform stationary mea sure (referred to as the rr-invariant measure) associated with the sta tistical space-fillings properties of the unstable invariant foliation in 2D differentiable area-preserving systems and derives a sequence o f analytical approximations for it. In fluid-dynamic problems, the w-m easure coincides with the intermaterial contact area density. [S0031-9 007(98)07503-6].