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 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 $\epsilon \mapsto h_{\epsilon }$ is Lipschitz continuous.

To appear in Communications in Mathematical Physics

References in corpus (2)

• Stochastically stable globally coupled maps with bistable thermodynamic limit
• Self consistent transfer operators. Invariant measures, convergence to equilibrium, linear response and control of the statistical properties

Cited by in corpus (1)

• Mean-field and fluctuations for hub dynamics in heterogeneous random networks