Globally Coupled Anosov Diffeomorphisms: Statistical Properties

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 system admits a unique physical invariant state, $$h_\varepsilon $$ h ε . Moreover, exponential convergence to equilibrium for suitable class distributions and show map $$\varepsilon \mapsto h_\varepsilon ↦ is Lipschitz continuous.