Intermittency generated by attracting and weakly repelling fixed points

Indagationes Mathematicae, vol. 34, pp. 457–476

Abstract

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay between a superexponentially attracting fixed point and an exponentially repelling fixed point. In this article we consider a closely related family of random systems with exponentially fast attraction to and polynomially fast repulsion from two fixed points, and show that such a phase transition still exists. The method of the proof however is different and relies on the construction of a suitable invariant set for the transfer operator.

Authors 1

1. Benthen Zeegers corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, University of Leiden, PO Box 9512, 2300 RA Leiden, The Netherlands