Absolute continuity of projected SRB measures of coupled Arnold cat map lattices

F. Bonetto; A. Kupiainen; J. L. Lebowitz

doi:10.1017/S0143385704000252

Absolute continuity of projected SRB measures of coupled Arnold cat map lattices

F. Bonetto, A. Kupiainen, J. L. Lebowitz

Mathematical physics

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

Abstract

We study a d-dimensional coupled map. lattice consisting of hyperbolic total automorphisms (Arnold cat maps) that are weakly coupled by an analytic map. We construct the Sinai-Ruelle-Bowen measure for this system and study its marginals on the tori. We prove that they are absolutely continuous with respect to Lebesgue measure if and only if the coupling satisfies a non-degeneracy condition.

Original language	English
Journal	Ergodic Theory and Dynamical Systems
Volume	25
Issue number	1
Pages (from-to)	59-88
Number of pages	30
ISSN	0143-3857
DOIs	https://doi.org/10.1017/S0143385704000252
Publication status	Published - 2005
MoE publication type	A1 Journal article-refereed

Fields of Science

111 Mathematics

Access to Document

10.1017/S0143385704000252

Cite this

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title = "Absolute continuity of projected SRB measures of coupled Arnold cat map lattices",

abstract = "We study a d-dimensional coupled map. lattice consisting of hyperbolic total automorphisms (Arnold cat maps) that are weakly coupled by an analytic map. We construct the Sinai-Ruelle-Bowen measure for this system and study its marginals on the tori. We prove that they are absolutely continuous with respect to Lebesgue measure if and only if the coupling satisfies a non-degeneracy condition.",

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T1 - Absolute continuity of projected SRB measures of coupled Arnold cat map lattices

AU - Bonetto, F.

AU - Kupiainen, A.

AU - Lebowitz, J. L.

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N2 - We study a d-dimensional coupled map. lattice consisting of hyperbolic total automorphisms (Arnold cat maps) that are weakly coupled by an analytic map. We construct the Sinai-Ruelle-Bowen measure for this system and study its marginals on the tori. We prove that they are absolutely continuous with respect to Lebesgue measure if and only if the coupling satisfies a non-degeneracy condition.

AB - We study a d-dimensional coupled map. lattice consisting of hyperbolic total automorphisms (Arnold cat maps) that are weakly coupled by an analytic map. We construct the Sinai-Ruelle-Bowen measure for this system and study its marginals on the tori. We prove that they are absolutely continuous with respect to Lebesgue measure if and only if the coupling satisfies a non-degeneracy condition.

KW - 111 Mathematics

U2 - 10.1017/S0143385704000252

DO - 10.1017/S0143385704000252

M3 - Article

VL - 25

SP - 59

EP - 88

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 1

ER -