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
✍ Scribed by Stefano Cerbelli; Massimiliano Giona; Alessandra Adrover; Mario M. Alvarez; Fernando J. Muzzio
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 914 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0960-0779
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✦ Synopsis
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 measure l w (intrinsically dierent 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 l w describes the nonuniform space-®lling properties of material lines under the recursive action of the transformation. The implications of the results for physically realizable mixing systems are also addressed. Ó 2000 Elsevier Science Ltd. All rights reserved. x v x xY yY tY y v y xY yY tY 1
where v x xY yY t and v y xY yY t are the Cartesian components of vxY yY t.