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

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

    Research output: Contribution to journalArticleScientificpeer-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 languageEnglish
    JournalErgodic Theory and Dynamical Systems
    Volume25
    Issue number1
    Pages (from-to)59-88
    Number of pages30
    ISSN0143-3857
    DOIs
    Publication statusPublished - 2005
    MoE publication typeA1 Journal article-refereed

    Fields of Science

    • 111 Mathematics

    Cite this

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    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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    Absolute continuity of projected SRB measures of coupled Arnold cat map lattices. / Bonetto, F.; Kupiainen, A.; Lebowitz, J. L.

    In: Ergodic Theory and Dynamical Systems, Vol. 25, No. 1, 2005, p. 59-88.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

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

    AU - Bonetto, F.

    AU - Kupiainen, A.

    AU - Lebowitz, J. L.

    PY - 2005

    Y1 - 2005

    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 -