Accessible Mandelbrot Sets in the Family zn+λ/zn

Paul Blanchard, Daniel Cuzzocreo, Robert L. Devaney*, Elizabeth Fitzgibbon

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

In this paper we prove the existence of infinitely many accessible Mandelbrot sets in the parameter plane for the family of maps (Formula presented.) when (Formula presented.). These are Mandelbrot sets for which the cusp of the main cardioid touches the outer boundary of the connectedness locus. We show that there is a unique such Mandelbrot set at the landing point of each external ray that is periodic under (Formula presented.).

Original languageEnglish (US)
Pages (from-to)49-66
Number of pages18
JournalQualitative Theory of Dynamical Systems
Volume15
Issue number1
DOIs
StatePublished - Apr 1 2016

Keywords

  • Complex dynamics
  • External rays
  • Internal rays
  • Julia set
  • Mandelbrot set

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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