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INICIO | 21 de abril de 2024
  

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

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
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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