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Globally coupled Anosov diffeomorphisms: Statistical properties (2208.02517v3)
Published 4 Aug 2022 in math.DS, math-ph, math.MP, and nlin.CD
Abstract: We study infinite systems of globally coupled Anosov diffeomorphisms with weak coupling strength. Using transfer operators acting on anisotropic Banach spaces, we prove that the coupled system admits a unique physical invariant state, $h_\varepsilon$. Moreover, we prove exponential convergence to equilibrium for a suitable class of distributions and show that the map $\varepsilon\mapsto h_\varepsilon$ is Lipschitz continuous.
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