Accessible Mandelbrot Sets in the Family zn+λ/zn

Paul Blanchard; Daniel Cuzzocreo; Robert L. Devaney; Elizabeth Fitzgibbon

doi:10.1007/s12346-015-0140-5

Accessible Mandelbrot Sets in the Family zⁿ+λ/zⁿ

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

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

2 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 language	English (US)
Pages (from-to)	49-66
Number of pages	18
Journal	Qualitative Theory of Dynamical Systems
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s12346-015-0140-5
State	Published - Apr 1 2016

Keywords

Complex dynamics
External rays
Internal rays
Julia set
Mandelbrot set

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1007/s12346-015-0140-5

Cite this

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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.).",

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