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Julia sets for holomorphic endomorphisms of ℂn

Published online by Cambridge University Press:  14 October 2010

Stefan-M. Heinemann
Stefan-M. Heinemann
Affiliation:
Institut für Mathematische Stochastik, Lotzestraβe 13, D-37083 Göttingen, Germany
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Abstract

We give a definition for a Julia set J(f) for generic classes of polynomial endomorphisms f: ℂn→ ℂn. For n = 1, our definition is equivalent to the usual one, which gives the points where the iterates of f do not form a normal family. Moreover, the Julia set J(f1 × … × fn) ⊂ ℂn for a product of one-dimensional polynomials fi: ℂ → ℂ turns out to be the product J(f1) × … × J(fn) of the associated Julia sets J(fi) ⊂ ℂ. For a special class of mappings f: ℂ2 → ℂ2 which is not of this simple type, the so-called Cantor skews, we investigate topological structure as well as measure theoretic aspects of the Julia sets obtained using our definition.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1275 - 1296
Copyright
Copyright © Cambridge University Press 1996

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