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ArticleOriginal scientific text

Title

Trees of visible components in the Mandelbrot set

Authors 1

Affiliations

  1. Department of Mathematics, University of Jyväskylä, P.O. Box 35, 40351 Jyväskylä, Finland

Abstract

We discuss the tree structures of the sublimbs of the Mandelbrot set M, using internal addresses of hyperbolic components. We find a counterexample to a conjecture by Eike Lau and Dierk Schleicher concerning topological equivalence between different trees of visible components, and give a new proof to a theorem of theirs concerning the periods of hyperbolic components in various trees.

Bibliography

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Fundamenta Mathematicae
2000/164/1
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Pages:
41-60
Main language of publication
English
Received
1999-04-27
Accepted
2000-01-18
Published
2000
Exact and natural sciences