On the Theory of Intermittency in 1D Maps

Abstract

The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Recently, we reported how the reinjection probability density (RPD) can be generalized. Estimation of the universal RPD is based on fitting a linear function to experimental or numerical data. Here we present an analytical approach to estimate the RPD. After this, we can get an analytic evaluation of the characteristic exponent traditionally used to characterize the intermittency type. The proposed theoretical method is general and very simple to use. It is compared with numerical computation, showing a good agreement between both. Our analytical results are compared with some celebrated classical numerical results on intermittency theory.