Some characteristics of the M function methodology to describe the reinjection process in chaotic intermittency

Abstract

The M function methodology allows calculating the statistical properties of intermittency in a broad class of one-dimensional maps. It has shown to be very accurate in type I, II, III and V intermittencies; and it also includes the uniform reinjection as a particular case. This paper studies some properties of the M function methodology. We establish the conditions that a reinjection probability density function must verify to obtain and we describe new pathological cases where the reinjection is not uniform, but the characteristic relation is the same that for uniform reinjection.