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 exponents
DOI: 10.1103/PhysRevA.37.1323

Citations: 21
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