On Accumulation of Stretching Rays - Cubic Polynomials with a Multiple Fixed Point

  • Willumsen, Pia B.N. (Project Manager)

    Project Details

    Description

    The project studies the
    parameter space for
    polynomials of degree k,
    where k is at least 3.
    More precisely, we study the
    boundary
    of the connectedness locus
    (the area in the
    parameter space, where the
    corresponding polynomials have
    a connected Julia set). A
    stretching ray is a real
    analytical curve in the
    complement of the
    connectedness locus. We are
    interested in the limiting
    behaviour of stretching rays
    when approaching the
    connectedness locus from the
    outside. Already a
    degree three polynomial with a
    multiple fixpoint exhibits
    interesting behaviour: An
    area in the boundary of the
    cubic connectedness locus
    has been found, where no
    stretching ray lands. The
    corresponding cubic polynomials
    are
    parabolic-attracting with
    both critical points
    in the
    immediate basin
    of the multiple fixpoint.
    We have established necessary
    conditions for the stretching
    ray through a polynomial to
    land in this area. The work is
    continued attempting to prove
    that stretching rays can land
    only on a specific graph in this
    area and that only a
    very special type of
    stretching rays can land on
    this graph. Keywords: Complex
    dynamical systems, parabolic
    cycles, stretching rays.
    StatusActive
    Effective start/end date01/01/1996 → …