Trees of visible components in the Mandelbrot set

Virpi Kauko
2000 Fundamenta Mathematicae  
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.
doi:10.4064/fm-164-1-41-60 fatcat:6vnrwh57f5hf5c6fstgmalpnym