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

Abstract

It has been rigorously shown in Ruelle (2005 Commun. Math. Phys. 258 445–53) 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 us to exhibit this pole from time series. We then apply the same analysis to the Hénon map and conjecture that the complex susceptibility also has a pole in the upper-half complex plane.