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(epsilon). Moreover, we prove exponential convergence to equilibrium for a suitable class of distributions and show that the map epsilon (sic)-> h(epsilon) is Lipschitz continuous.
Bahsoun, W., Liverani, C., Sélley, F.m. (2023). Globally coupled Anosov diffeomorphisms: statistical properties. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 400(3), 1791-1822 [10.1007/s00220-022-04631-3].
Globally coupled Anosov diffeomorphisms: statistical properties
Carlangelo Liverani;
2023-01-01
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(epsilon). Moreover, we prove exponential convergence to equilibrium for a suitable class of distributions and show that the map epsilon (sic)-> h(epsilon) is Lipschitz continuous.File in questo prodotto:
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