Pesin-type relation for subexponential instability

Details Pesin-type relation for subexponential instability Pesin-type relation for subexponential instability

2011-09-26

arxiv.org/abs/1109.5419v2

J. Stat. Mech. (2012) P03010

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/1742-5468/2012/03/P03010

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 Zweim\"uller, 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 Zweim\"uller'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.

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