Pesin-type relation for subexponential instability

Abstract

We address here the problem of extending the Pesin relation among positive Lyapunov exponents and the Kolmogorov-Sinai entropy to the case of dynamical systems exhibiting subexponential instabilities. By using a recent rigorous result due to Zweimüller, we show that the usual Pesin relation can be extended straightforwardly for weakly chaotic one-dimensional systems of the Pomeau-Manneville type, provided one introduces a convenient subexponential generalization of the Kolmogorov-Sinai entropy. We show, furthermore, that Zweimüller's result provides an efficient prescription for the evaluation of the algorithm complexity for such systems. Our results are confirmed by exhaustive numerical simulations. We also point out and correct a misleading extension of the Pesin relation based on the Krengel entropy that has appeared recently in the literature.

10 pages, 4 figures. Final version to appear in Journal of Statistical Mechanics (JSTAT)

References in corpus (5)

• Pesin-Type Identity for Weak Chaos
• Subexponential instability implies infinite invariant measure
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Cited by in corpus (5)

• Thermodynamic phase transitions for Pomeau-Manneville maps
• Number of first-passage times as a measurement of information for weakly chaotic systems
• Exact invariant measures: How the strength of measure settles the intensity of chaos
• Does an intermittent dynamical system remain (weakly) chaotic after drilling in a hole?
• From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling