Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
| dc.creator | Poggi-Corradini, Pietro | |
| dc.date | 2003-08-06 | |
| dc.date.accessioned | 2026-07-07T05:00:12Z | |
| dc.date.available | 2026-07-07T05:00:12Z | |
| dc.description | A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk. 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. | |
| dc.description | 32 pages, to appear in Revista Matematica Iberoamericana | |
| dc.identifier | https://arxiv.org/abs/math/0308060 | |
| dc.identifier | http://arxiv.org/abs/math/0308060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68265 | |
| dc.subject | Complex Variables | |
| dc.subject | 30D05 | |
| dc.title | Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk | |
| dc.type | text |