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

Pietro Poggi-Corradini (2003)

Revista Matemática Iberoamericana

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...

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