Algorithmic information for intermittent systems with an indifferent fixed point

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Measuring the average information that is necessary to describe the behaviour of a dynamical system leads to a generalization of the Kolmogorov-Sinai entropy. This is particularly interesting when the system has null entropy and the information increases less than linearly with respect to time. We consider two classes of maps of the interval with an indifferent fixed point at the origin and an infinite natural invariant measure. We calculate that the average information that is necessary to describe the behaviour of its orbits increases with time $n$ approximately as $n^α$, where $α<1$ depends only on the asymptotic behaviour of the map near the origin.
24 pages, 2 figures

Keywords

Dynamical Systems

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/70344

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403070
 http://arxiv.org/abs/math/0403070

Collections

arXiv