Título inglés |
Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk. |
Título español |
Sucesiones de retro-iteraciones con pasos hiperbólicos acotatados para autoaplicaciones analíticas del disco unidad. |
Autor/es |
Poggi-Corradini, Pietro |
Organización |
Dep. Math. Cardwell Hall Kansas State Univ., Manhattan (Kansas), Estados Unidos |
Revista |
0213-2230 |
Publicación |
2003, 19 (3): 943-970, 9 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
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. |
Clasificación UNESCO |
120209 |
Palabras clave español |
Funciones de variable compleja ; Funciones analíticas ; Iteración ; Punto fijo ; Ecuaciones funcionales |
Código MathReviews |
MR2053569 |
Código Z-Math |
Zbl 1057.30023 |
Acceso al artículo completo |