Globally Coupled Anosov Diffeomorphisms: Statistical Properties

Communications in Mathematical Physics, vol. 400, pp. 1791–1822

Abstract

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, $$h_\varepsilon $$ h ε . Moreover, we prove exponential convergence to equilibrium for a suitable class of distributions and show that the map $$\varepsilon \mapsto h_\varepsilon $$ ε ↦ h ε is Lipschitz continuous.

Authors 3

1. Wael Bahsoun corresponding

   Loughborough University

   Affiliation as printed

   Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK

2. Carlangelo Liverani

   University of Rome Tor Vergata

   Affiliation as printed

   Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133, Roma, Italy

3. Fanni M. Sélley Aachen

   Leiden University

   Affiliation as printed

   Mathematical Institute of Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands