Locating Pollicott-Ruelle resonances in chaotic dynamical systems: A class of numerical schemes

Abstract

A class of numerical methods to determine Pollicott-Ruelle resonances in chaotic dynamical systems is proposed. This is achieved by relating some existing procedures which make use of Pade approximants and interpolating exponentials to both the memory function techniques used in the theory of relaxation and the filter diagonalization method used in the harmonic inversion of time correlation functions. This relationship leads to a theoretical framework in which all these methods become equivalent and which allows for new and improved numerical schemes.