Homeomorphisms Between Limbs of the Mandelbrot Set

Bodil Branner, Nuria Fagella

    Research output: Contribution to journalJournal articleResearchpeer-review


    Using a family of higher degree polynomials as a bridge, together with complex surgery techniques, we construct a homeomorphism between any two limbs of the Mandelbrot set of equal denominator. Induced by these homeomorphisms and complex conjugation, we obtain an involution between each limb and itself. whose fixed points form a topological arc. All these maps have counterparts at the combinatorial level relating corresponding external arguments. Assuming local connectivity of the Mandelbrot set we may conclude that the constructed homeomorphisms between limbs are compatible with the embeddings of the limbs in the plane. As usual we plough in the dynamical planes and harvest in the parameter space.
    Original languageEnglish
    JournalJournal of Geometric Analysis
    Issue number3
    Pages (from-to)327-390
    Publication statusPublished - 1999

    Cite this