Non-locally Connected Quadratic Julia Sets

  • Sørensen, Dan Erik Krarup (Project Manager)
  • Branner, Bodil (Project Participant)
  • Willumsen, Pia B.N. (Project Participant)
  • Douady, Adrien (Project Participant)
  • Hubbard, John H. (Project Participant)
  • Petersen, Carsten Lunde (Project Participant)

    Project Details

    Description

    Work is done with non-linear
    dynamical systems, which
    appears from iterating with a
    complex, quadratic polynomial.
    The main purpose is to
    increase the understanding of
    the dynamic, geometry and
    topology for polynomials with
    locally connected Julia set.
    As an example, the behaviour
    of certain external rays under
    repeated parabolic
    pertubations are investigated.
    As the most important side
    results we should mentioned
    the achievement of the first
    known examples of connected,
    but not curve-connected Julia
    sets, as well as non-robust,
    renormalizeable (infinitely
    many times) quadratic
    polynomials. Present work is
    considering the possibility
    to relate the polynomial
    classes found to the
    so-called Diophantic
    conditions in the theory of
    numbers and the possibility
    to find quadratic Julia sets
    with positive measure.
    Keywords: External rays,
    local connectedness,
    robustness and Julia sets.
    StatusFinished
    Effective start/end date01/09/199631/08/1997

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