Keplerian shear in ergodic theory
[Le cisaillement keplérien en théorie ergodique]
Thomine, Damien1
1 Laboratoire de Mathématiques d’Orsay, LMO / UMR 8628, Bâtiment 307, Faculté des Sciences d’Orsay, Université Paris-Sud, F-91405 Orsay Cedex
Annales Henri Lebesgue, Tome 3 (2020), pp. 649-676.

Le cisaillement keplérien est une propriété commune à de nombreux systèmes intégrables. Nous considérons ce phénomène du point de vue de la théorie ergodique, en tant que propriété de mélange conditionnellement à une tribu invariante. Dans ce contexte, nous donnons des conditions suffisantes assurant que le cisaillement keplérien apparaisse dans un système dynamique donné. De plus, nous discutons la généricité de ce phénomène et, dans certains cas, sa vitesse. Quelques exemples supplémentaires, qui ne sont pas de nature hamiltonienne, sont donnés.

Many integrable physical systems exhibit Keplerian shear. We look at this phenomenon from the point of view of ergodic theory, where it can be seen as mixing conditionally to an invariant σ-algebra. In this context, we give a sufficient criterion for Keplerian shear to appear in a system, investigate its genericity and, in a few cases, its speed. Some additional, non-Hamiltonian, examples are discussed.

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DOI : 10.5802/ahl.42
Classification : 37A25, 37J35
Mots clés : integrable system, mixing, speed of mixing
Thomine, Damien 1

1 Laboratoire de Mathématiques d’Orsay, LMO / UMR 8628, Bâtiment 307, Faculté des Sciences d’Orsay, Université Paris-Sud, F-91405 Orsay Cedex 
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Thomine, Damien. Keplerian shear in ergodic theory. Annales Henri Lebesgue, Tome 3 (2020), pp. 649-676. doi : 10.5802/ahl.42. http://www.numdam.org/articles/10.5802/ahl.42/

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