Algorithmic information for intermittent systems with an indifferent fixed point

Details Algorithmic information for intermittent systems with an indifferent fixed point Algorithmic information for intermittent systems with an indifferent fixed point

2004-03-03

arxiv.org/abs/math/0403070v1

Mathematics

Dynamical Systems

24 pages, 2 figures

Scientific paper

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^\alpha $, where $\alpha<1$ depends only on the asymptotic behaviour of the map near the origin.

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