Resonances of chaotic dynamical systems

Abstract

We present analytic properties of the power spectrum for a class of chaotic dynamical systems (Axiom-A systems). The power spectrum is meromorphic in a strip; the position of the poles (resonances) depends on the system considered, but only their residues depend on the observable monitored. In relation with these results we also discuss the exponential or nonexponential decay of correlation functions at infinity. In conclusion, it appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general).