A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents

Huyi Hu; Yakov Pesin; Anna Talitskaya

doi:10.1007/s00220-012-1602-0

A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents

Huyi Hu, Yakov Pesin, Anna Talitskaya

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Abstract

We show that there exists a C^∞ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset G of not full volume and has zero Lyapunov exponent on the complement of G.

Original language	English (US)
Pages (from-to)	331-378
Number of pages	48
Journal	Communications In Mathematical Physics
Volume	319
Issue number	2
DOIs	https://doi.org/10.1007/s00220-012-1602-0
State	Published - Apr 2013

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-012-1602-0

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title = "A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents",

abstract = "We show that there exists a C∞ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset G of not full volume and has zero Lyapunov exponent on the complement of G.",

author = "Huyi Hu and Yakov Pesin and Anna Talitskaya",

note = "Funding Information: H. H. was partially supported by NSF grant DMS-0503870; Ya. P. was partially supported by the NSF grant DMS-1101165.",

year = "2013",

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AU - Hu, Huyi

AU - Pesin, Yakov

AU - Talitskaya, Anna

N1 - Funding Information: H. H. was partially supported by NSF grant DMS-0503870; Ya. P. was partially supported by the NSF grant DMS-1101165.

PY - 2013/4

Y1 - 2013/4

N2 - We show that there exists a C∞ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset G of not full volume and has zero Lyapunov exponent on the complement of G.

AB - We show that there exists a C∞ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset G of not full volume and has zero Lyapunov exponent on the complement of G.

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A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents

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