Globally Coupled Anosov Diffeomorphisms: Statistical Properties
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, $$h_\varepsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>h</mml:mi> <mml:mi>ε</mml:mi> </mml:msub> </mml:math> . Moreover, we prove exponential convergence to …