Transfer Operators for Coupled Analytic Maps

1997/11/18 by Torsten Fischer, Fischer, Torsten, Hans Henrik Rugh +1 · 1 citation
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Functional Equations Stability Results #Mathematical Dynamics and Fractals #advanced mathematical theories #chao-dyn #nlin.CD

paper · pdf · doi:10.48550/arxiv.chao-dyn/9711018

44 pages, Latex + 2 post script figures

arxiv created 1997/11/18 · openalex publication_date 1997/11/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider analytic coupled map lattices over \Z^d with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures with analytic, exponentially bounded finite dimensional marginals. Using residue calculus and `cluster expansion'-like techniques we define transfer operators on these Banach spaces. For these we get a unique probability measure that exhibits exponential decay of correlations.

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• Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method

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