Dynamics of polynomials with disconnected Julia sets
Nathaniel D. Emerson - Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States (email)
Abstract: 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.
Keywords: Complex dynamical systems, Julia set.
Received: May 2002; Revised: December 2002; Published: April 2003.
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