Pesin-type relation for subexponential instability

TL;DR

This paper extends the Pesin relation to systems with subexponential instability, using recent mathematical results to connect Lyapunov exponents and entropy in weakly chaotic systems, confirmed by numerical simulations.

Contribution

It provides a rigorous extension of the Pesin relation for subexponential systems using Zweimüller's result, and corrects previous misconceptions based on Krengel entropy.

Findings

Extended Pesin relation for subexponential systems.

Validated the relation through numerical simulations.

Provided an efficient method to evaluate algorithm complexity.

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 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.