Accessible Mandelbrot Sets in the Family z(n) + lambda/z(n)

作者：Blanchard Paul; Cuzzocreo Daniel; Devaney Robert L^*; Fitzgibbon Elizabeth

来源：Qualitative Theory of Dynamical Systems, 2016, 15(1): 49-66.

DOI：10.1007/s12346-015-0140-5

• Mandelbrot set
• Julia set
• Complex dynamics
• External rays
• Internal rays

In this paper we prove the existence of infinitely many accessible Mandelbrot sets in the parameter plane for the family of maps z(n) +lambda/z(n) 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 theta bar right arrow n theta.

• 出版日期2016-4