Buried Sierpinski curve Julia sets

Pages: 1035 - 1046, Volume 13, Issue 4, November 2005

doi:10.3934/dcds.2005.13.1035       Abstract        Full Text (254.8K)       Related Articles

Robert L. Devaney - Department of Mathematics, Boston University, Boston, MA 02215, United States (email)
Daniel M. Look - Department of Mathematics, Boston University, Boston, MA 02215, United States (email)

Abstract: 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, Sierpinski curve, rational map.
Mathematics Subject Classification:  Primary: 37F45; Secondary: 37F20.

Received: September 2004;      Revised: March 2005;      Published: August 2005.