Accessible Mandelbrot Sets in the Family zn + λ/zn

Paul Blanchard ^[1] ; Daniel Cuzzocreo ^[1] ; Robert L. Devaney ^[1] ; Elizabeth Fitzgibbon ^[1]
1. [1] Boston University
  
  Boston University
  
  City of Boston, Estados Unidos
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 1, 2016, págs. 49-66
Idioma: inglés
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Resumen
- In this paper we prove the existence of infinitely many accessible Mandelbrot sets in the parameter plane for the family of maps zn + λ/zn when n > 1.
  
  These are Mandelbrot sets for which the cusp of the main cardioid touches the outer boundary of the connectedness locus. We show that there is a unique such Mandelbrot set at the landing point of each external ray that is periodic under θ → nθ.