Application of hyperbolic dynamics to physics: Some problems and conjectures

Abstract

The long time behavior of smooth dynamical systems is, in good cases, given by an SRB measure ρ \rho . The measure ρ \rho is expected often to have very discontinuous dependence on parameters of the dynamical system. This is a very unsatisfactory situation for physical applications, where one would like to differentiate ρ \rho with respect to parameters. Here we propose a solution to this difficulty, based on analytic continuation in a frequency variable ω \omega .