Correlation functions and generalized Lyapunov exponents
Year: 1988
Authors: Badii R., Heinzelmann K., Meier P.F., Politi A.
Autors Affiliation: Institut fur Theoretische Physik, Universitat Zurich, CH-8001, Zurich, Switzerland;
Physik-Institut, Universitat Zurich, CH-8001, Zurich, Switzerland;
Istituto Nazionale di Ottica, I-50125 Firenze, Italy
Abstract: Correlation functions of one- and two-dimensional piecewise linear maps are analytically investigated. The asymptotic time behavior is shown to be given by the average inverse multiplier 〈μ1-1(τ)〉, for one-dimensional maps with absolutely continuous invariant measure. The decay rate γ coincides with the generalized Lyapunov exponent Λ(scrq) at scrq=2, if the sign of the multiplier does not change during the time evolution, while, in general, it is larger than Λ(2). The analysis of two-dimensional maps reveals the importance of the average second multiplier 〈μ2(τ)〉 and of the average ratio 〈μ2(τ)/μ1(τ)〉 which, in some cases, can provide the leading long-time contribution.
Journal/Review: PHYSICAL REVIEW A
Volume: 37 (4) Pages from: 1323 to: 1328
KeyWords: Lyapunov exponentsDOI: 10.1103/PhysRevA.37.1323Citations: 21data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-24References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here