This article analyzes the global invariant properties of a class of exactly solvable area-preserving mixing transformations of the two dimensional torus. Starting from the closed-form solution of the expanding sub-bundle, a nonuniform stationary measures μw (intrinsically different from the ergodic one) is derived analytically, providing a concrete example for which the connections between geometrical and measure-theoretical approaches to chaotic dynamics can be worked out explicitly. It is shown that the measure μw describes the nonuniform space-filling properties of material lines under the recursive action of the transformation. The implications of the results for physically realizable mixing systems are also addressed.
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 / Cerbelli, Stefano; Giona, Massimiliano; Adrover, Alessandra; Mario M., Alvarez; Fernando J., Muzzio. - In: CHAOS, SOLITONS AND FRACTALS. - ISSN 0960-0779. - 11:4(2000), pp. 607-630. [10.1016/s0960-0779(98)00171-4]
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
CERBELLI, Stefano;GIONA, Massimiliano;ADROVER, Alessandra;
2000
Abstract
This article analyzes the global invariant properties of a class of exactly solvable area-preserving mixing transformations of the two dimensional torus. Starting from the closed-form solution of the expanding sub-bundle, a nonuniform stationary measures μw (intrinsically different from the ergodic one) is derived analytically, providing a concrete example for which the connections between geometrical and measure-theoretical approaches to chaotic dynamics can be worked out explicitly. It is shown that the measure μw describes the nonuniform space-filling properties of material lines under the recursive action of the transformation. The implications of the results for physically realizable mixing systems are also addressed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.