The correlation spectrum for hyperbolic analytic maps

Abstract

The author introduces a class of analytic hyperbolic maps and prove that the time correlation functions associated with analytic observables have a well-defined spectrum satisfying exponential bounds. From the stability of the fixed points of the iterated map he constructs a Fredholm determinant which is an entire function of a complex variable and shows that from its roots he can calculate the spectral values. This paper extends previously obtained results for purely expanding analytic maps and analytic observables as well as for C1+ in Axiom A diffeomorphisms and Holder continuous observables. It gives a new, improved, approach to the case of real analytic Axiom A systems and analytic observables.