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July  2005, 13(4): 1035-1046. doi: 10.3934/dcds.2005.13.1035

Buried Sierpinski curve Julia sets

Robert L. Devaney 1, and  Daniel M. Look 1,

1. 

Department of Mathematics, Boston University, Boston, MA 02215, United States, United States

Received  September 2004 Revised  March 2005 Published  August 2005

In this paper we prove the existence of a new type of Sierpinski curve Julia set for certain families of rational maps of the complex plane. In these families, the complementary domains consist of open sets that are preimages of the basin at $\infty$ as well as preimages of other basins of attracting cycles.
Keywords: Julia sets, rational map., Sierpinski curve.
Mathematics Subject Classification: Primary: 37F45; Secondary: 37F2.
Citation: Robert L. Devaney, Daniel M. Look. Buried Sierpinski curve Julia sets. Discrete & Continuous Dynamical Systems, 2005, 13 (4) : 1035-1046. doi: 10.3934/dcds.2005.13.1035
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