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On the Definition of SRB-Measures¶for Coupled Map Lattices

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Abstract:

We consider SRB-measures of coupled map lattices. The emphasis is given to a definition according to which a SRB-measure is an invariant probability measure whose projections onto finite-dimensional subsystems are absolutely continuous with respect to the Lebesgue measure. We show that coupled map lattices which are close to an uncoupled expanding map have typically an infinite number of SRB-measures. In particular, we give a counterexample to the Bricmont–Kupiainen conjecture.

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  1. University of Jyväskylä, Department of Mathematics, P.O. Box 35, 40351 Jyväskylä, Finland.¶E-mail: esaj@math.jyu.fi; amj@math.jyu.fi, , , , , , FI

    Esa Järvenpää & Maarit Järvenpää

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  1. Esa Järvenpää
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  2. Maarit Järvenpää
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Received: 23 June 2000 / Accepted: 4 January 2001

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Järvenpää, E., Järvenpää, M. On the Definition of SRB-Measures¶for Coupled Map Lattices. Commun. Math. Phys. 220, 1–12 (2001). https://doi.org/10.1007/s002200100432

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  • DOI: https://doi.org/10.1007/s002200100432

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