Dynamics of polynomials with disconnected Julia sets

Pages: 801 - 834, Volume 9, Issue 4, July 2003

doi:10.3934/dcds.2003.9.801       Abstract        Full Text (361.1K)       Related Articles

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.
Mathematics Subject Classification:  37F50, 37F10.

Received: May 2002;      Revised: December 2002;      Published: April 2003.