July  2003, 9(4): 801-834. doi: 10.3934/dcds.2003.9.801

Dynamics of polynomials with disconnected Julia sets

1. 

Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States

Received  May 2002 Revised  December 2002 Published  April 2003

We study the structure of disconnected polynomial Julia sets. We consider polynomials with an arbitrary number of non-escaping critical points, of arbitrary multiplicity, which interact non-trivially. We use a combinatorial system of a tree with dynamics to give a sufficient condition for the Julia set a polynomial to be an area zero Cantor set. We show that there exist uncountably many combinatorially inequivalent polynomials, which satisfy this condition and have multiple non-escaping critical points, each of which accumulates at all the non-escaping critical points.
Citation: Nathaniel D. Emerson. Dynamics of polynomials with disconnected Julia sets. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 801-834. doi: 10.3934/dcds.2003.9.801
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