Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.

Poggi-Corradini, Pietro. "Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.." Revista Matemática Iberoamericana 19.3 (2003): 943-970. <http://eudml.org/doc/39735>.

@article{Poggi2003,
abstract = {A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk 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.},
author = {Poggi-Corradini, Pietro},
journal = {Revista Matemática Iberoamericana},
keywords = {Funciones de variable compleja; Funciones analíticas; Iteración; Punto fijo; Ecuaciones funcionales; forward iterates; back iteration sequence; Denjoy-Wolff theorem},
language = {eng},
number = {3},
pages = {943-970},
title = {Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.},
url = {http://eudml.org/doc/39735},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Poggi-Corradini, Pietro
TI - Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 3
SP - 943
EP - 970
AB - A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk 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.
LA - eng
KW - Funciones de variable compleja; Funciones analíticas; Iteración; Punto fijo; Ecuaciones funcionales; forward iterates; back iteration sequence; Denjoy-Wolff theorem
UR - http://eudml.org/doc/39735
ER -