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December, 2003 Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
Pietro Poggi-Corradini
Rev. Mat. Iberoamericana 19(3): 943-970 (December, 2003).

Abstract

A lot is known about the forward iterates of an analytic function which is bounded by $1$ in modulus on the unit disk $\mathbb{D}$. The Denjoy-Wolff Theorem describes their convergence properties and several authors, from the 1880's to the 1980's, have provided conjugations which yield very precise descriptions of the dynamics. Backward-iteration sequences are of a different nature because a point could have infinitely many preimages as well as none. However, if we insist in choosing preimages that are at a finite hyperbolic distance each time, we obtain sequences which have many similarities with the forward-iteration sequences, and which also reveal more information about the map itself. In this note we try to present a complete study of backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.

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Pietro Poggi-Corradini. "Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk." Rev. Mat. Iberoamericana 19 (3) 943 - 970, December, 2003.

Information

Published: December, 2003
First available in Project Euclid: 20 February 2004

zbMATH: 1057.30023
MathSciNet: MR2053569

Subjects:
Primary: 30D05 , 30D50 , 39B32

Keywords: backward-iteration , bounded steps

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.19 • No. 3 • December, 2003
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