Quasi-conformal Surgery

    Project Details

    Description

    The technique of quasi-
    conformal surgery in
    holomorphic dynamics was
    initiated by Sullivan,
    Douady, Hubbard and
    Shishikura in the early
    eighties. The method is to
    create new dynamical systems
    out of some given ones, by
    changing not only the
    dynamical plane (through
    cutting and sewing) and the
    map defining the dynamical
    system, but also the complex
    structure of the new
    dynamical plane. The theory
    of quasi-conformal mappings
    is the basic tool. Surgery
    techniques appear to be
    particularly successful, when
    two families of maps can be
    related in such a way that
    dynamical similarities are
    transferred to similarities
    between structures in the
    corresponding parameter
    spaces. Homeomorphisms
    between p/q-limbs of the
    Mandelbrot set, with fixed
    denominator q, have been
    obtained. Generalizations are
    currently being investigated.
    StatusActive
    Effective start/end date01/07/1993 → …

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