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Meromorphic multifunctions in complex dynamics

Published online by Cambridge University Press:  19 September 2008

L. Baribeau  and
T. J. Ransford
L. Baribeau
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1 SB, UK
T. J. Ransford
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1 SB, UK
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Abstract

Let {RA} be an analytic family of rational maps and denote by j(λ) the Julia set of Rλ. We prove that the upper semicontinuous regularization j(λ) of j(λ) (which coincides with j(λ) for all λ in a dense open set) is a meromorphic multifunction, and give applications that illustrate the instability of Julia sets. In a similar vein, we also consider forward orbits of critical points and limit sets of Kleinian groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 39 - 52
Copyright
Copyright © Cambridge University Press 1992

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