Classification criterion for dynamical systems in intermittent chaos

Abstract

Intermittent chaos is investigated by means of an extended version of the statistical-mechanical formalism developed by Sato and Honda [Phys. Rev. A 42, 3233 (1990)]. An exact criterion is given to classify intermittent systems from the point of view of the generated chaotic phases based on the probability distribution of laminar lengths which is an explicitly measurable quantity from the time series. This criterion provides us with the generalization of the concept of intermittency which broadens the class of critical phenomena associated with the spectrum of dynamical entropies. It is shown that, in contrast to general belief, the presence of the regular chaos phase (i.e., vanishing R\'enyi entropies for inverse temperatures q>1) is not necessarily related to intermittency. In fact, the absence of any phase transition or the appearance of an anomalous chaos phase (i.e., infinite R\'enyi entropies for q0) is also possible in intermittent systems. We derive how the pressure, computed from a series of signals of increasing length, approaches its asymptotic value in the regular and anomalous phases.