Invariant properties of a class of exactly solvable mixing transformations- A measure-theoretical approach to model the evolution of material lines advected by chaotic flows

This article analyzes the global invariant properties of a class of exactly solvable area-preserving mixing transformations of the two dimensional tor us. Starting from the closed-form solution of the expanding sub-bundle, a n onuniform stationary measure mu(w) (intrinsically different from the ergodi c one) is derived analytically, providing a concrete example for which the connections between geometrical and measure-theoretical approaches to chaot ic dynamics can be worked out explicitly. It is shown that the measure mu(w ) describes the nonuniform space-filling properties of material lines under the recursive action of the transformation. The implications of the result s for physically realizable mixing systems are also addressed. (C) 2000 Els evier Science Ltd. All rights reserved.