Parabolic dynamics according to Maurice Heins

Abstract

This paper, based upon an unpublished manuscript by Maurice Heins, answers a question posed by Valiron about the dynamics of parabolic self-maps of the unit disk in the complex plane, considerably simplifying arguments previously used for answering the same question. The main new tool introduced is the notion of left straightening of a sequence of iterates, that can be effectively employed for studying the hyperbolic step of a parabolic map.

This paper is dedicated to the memory of Marek Jarnicki. To appear in Complex Analysis and Its Synergies; this version takes into account the comments of the referee