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

Research output: Contribution to journal › Article › peer-review

73 Scopus citations

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

Cite this

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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)",

volume = "14",

pages = "757--785",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

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T1 - Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems

AU - Katok, Anatole

AU - Burns, Keith

PY - 1994/12

Y1 - 1994/12

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.

UR - https://www.scopus.com/pages/publications/0000612131

UR - https://www.scopus.com/pages/publications/0000612131#tab=citedBy

U2 - 10.1017/S0143385700008142

DO - 10.1017/S0143385700008142

M3 - Article

AN - SCOPUS:0000612131

SN - 0143-3857

VL - 14

SP - 757

EP - 785

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 4

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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