Year: 2004
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Bonanno, Claudio, Galatolo, Stefano
Institutions: Università di Camerino, University of Pisa
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1645972190