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

Revista Matemática Iberoamericana (2003)

- Volume: 19, Issue: 3, page 943-970
- ISSN: 0213-2230

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topPoggi-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 -