Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems

Anatole Katok; Keith Burns

doi:10.1017/S0143385700008142

Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems

Anatole Katok, Keith Burns

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Abstract

We establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C^∞ Riemannian metric whose geodesic flow is Bernoulli.

Original language	English (US)
Pages (from-to)	757-785
Number of pages	29
Journal	Ergodic Theory and Dynamical Systems
Volume	14
Issue number	4
DOIs	https://doi.org/10.1017/S0143385700008142
State	Published - Dec 1994

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1017/S0143385700008142

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title = "Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems",

abstract = "We establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C∞ Riemannian metric whose geodesic flow is Bernoulli.",

author = "Anatole Katok and Keith Burns",

year = "1994",

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doi = "10.1017/S0143385700008142",

language = "English (US)",

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AU - Burns, Keith

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N2 - We establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C∞ Riemannian metric whose geodesic flow is Bernoulli.

AB - We establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C∞ Riemannian metric whose geodesic flow is Bernoulli.

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JF - Ergodic Theory and Dynamical Systems

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ER -

Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems

Abstract

All Science Journal Classification (ASJC) codes

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