Article thumbnail
Location of Repository

Local connectivity of the Julia set of real polynomials

By Genadi Levin and Sebastian van Strien

Abstract

One of the main questions in the field of complex dynamics is the question whether the Mandelbrot set is locally connected, and related to this, for which maps the Julia set is locally connected. In this paper we shall prove the following Main Theorem: Let $f$ be a polynomial of the form $f(z)=z^d +c$ with $d$ an even integer and $c$ real. Then the Julia set of $f$ is either totally disconnected or locally connected. In particular, the Julia set of $z^2+c$ is locally connected if $c \in [-2,1/4]$ and totally disconnected otherwise

Topics: Mathematics - Dynamical Systems
Year: 1995
OAI identifier: oai:arXiv.org:math/9504227

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.