Does the complex susceptibility of the Henon map have a pole in the upper-half plane ? A numerical investigation

Abstract

It has been rigorously shown in [Ruelle, 2005] that the complex susceptibility of chaotic maps of the interval can have a pole in the upper-half complex plane. We develop a numerical procedure allowing to exhibit this pole from time series. We then apply the same analysis to the Henon map and conjecture that the complex susceptibility has also a pole in the upper-half complex plane.