Trees of visible components in the Mandelbrot set

Tom 164 / 2000

Virpi Kauko Fundamenta Mathematicae 164 (2000), 41-60 DOI: 10.4064/fm-164-1-41-60

Streszczenie

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.

Autorzy

  • Virpi Kauko

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