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arXiv · 0910.5451

Backward iteration in the unit ball

Olena Ostapyuk
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Abstract

We will consider iteration of an analytic self-map $f$ of the unit ball in $\mathbb{C}^N$. Many facts were established about such dynamics in the 1-dimensional case (i.e. for self-maps of the unit disk), and we will generalize some of them in higher dimensions. In particular, in the case when $f$ is hyperbolic or elliptic, it will be shown that backward-iteration sequences with bounded hyperbolic step converge to a point on the boundary. These points will be called boundary repelling fixed points and will possess several nice properties. At each isolated boundary repelling fixed point we will also construct a (semi) conjugation of $f$ to an automorphism via an analytic intertwining map. We will finish with some new examples.

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Olena Ostapyuk. 2009-10-28. Backward iteration in the unit ball. https://arxiv.org/abs/0910.5451

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