Measuring the average information that is necessary to describe the behavior 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 a class of maps of the interval with an indifferent fixed point at the origin and an infinite natural invariant measure. We show that the average information that is necessary to describe the behavior of the orbits increases with time n approximately as n^α, where α<1 depends only on the asymptotic behavior of the map near the origin.
Algorithmic information for interval maps with an indifferent fixed point and infinite invariant measure
BONANNO, CLAUDIO;GALATOLO, STEFANO
2004-01-01
Abstract
Measuring the average information that is necessary to describe the behavior 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 a class of maps of the interval with an indifferent fixed point at the origin and an infinite natural invariant measure. We show that the average information that is necessary to describe the behavior of the orbits increases with time n approximately as n^α, where α<1 depends only on the asymptotic behavior of the map near the origin.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.