Backward iteration in the unit ball

2009/10/28 by Olena Ostapyuk, Ostapyuk, Olena
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.0910.5451

Abstract

We will consider iteration of an analytic self-map f of the unit ball in 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.

Related

• Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
• Backward orbits in the unit ball
• Backward iteration in strongly convex domains
• Canonical models for the forward and backward iteration of holomorphic maps
• Realizing arbitrary d-dimensional dynamics by renormalization of C^d-perturbations of identity