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

Bruno Cessac (1, 2)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 ODYSSEE - Computer and biological vision

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Systèmes dynamiques [math.DS]; Dynamique Chaotique [nlin.CD]; Mécanique statistique [cond-mat.stat-mech]

Bruno Cessac. Does the complex susceptibility of the Henon map have a pole in the upper-half plane ? A numerical investigation. Nonlinearity, 2007, 20, pp.2883-2895. ⟨10.1088/0951-7715/20/12/007⟩. ⟨hal-00188795⟩