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Arbieto A., Matheus C., Pacifico M.J. — The Bernoulli Property for Weakly Hyperbolic Systems
Arbieto A., Matheus C., Pacifico M.J. — The Bernoulli Property for Weakly Hyperbolic Systems



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Название: The Bernoulli Property for Weakly Hyperbolic Systems

Авторы: Arbieto A., Matheus C., Pacifico M.J.

Аннотация:

Journal of Statistical Physics, Vol. 117, Nos. 1/2, October 2004. p. 243-260.
A dynamical system is called partially hyperbolic if it exhibits three invariant directions, one unstable (expanding), one stable (contracting) and one central direction (somewhere in between the other two). We prove that topologically mixing partially hyperbolic diffeomorphisms whose central direction is non-uni-formly contracting (negative Lyapunov exponents) almost everywhere have the Bernoulli property: the system is equivalent to an i. i. d. (independently identically distributed) random process. In particular, these systems are mixing: correlations of integrable functions go to zero as time goes to infinity.
We also extend this result in two different ways. Firstly, for 3-dimensional diffeomorphisms, if one requires only non-zero (instead of negative) Lyapunov exponents then one still gets a quasi-Bernoulli property. Secondly, if one assumes accessibility (any two points are joined by some path whose legs are stable segments and unstable segments) then it suffices to requires the mostly contracting property on a positive measure subset, to obtain the same conclusions.


Язык: en

Рубрика: Физика/

Тип: Статья

Статус предметного указателя: Неизвестно

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Год издания: 2004

Количество страниц: 18

Добавлена в каталог: 20.10.2013

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