Asymptotic Values, Prepoles, and Periodic Points

Curves of parameter values for which an asymptotic value of F,(z) = 1 + e-z lies on a pre-pole of arbitrary order are found through an iterative method. Some of these curves are shown to be real analytic. Regions bounded by certain pairs of consecutive curves of parameter values are found where periodic cycles exist for F,. Numerically some of these periodic cycles are shown to be attracting and the corresponding Julia sets are depicted.

• Type: Journal
• Year: 2010
• Where: IJBC
• Authors: Jared Whitehead, Lennard Bakker
• Keywords: Asymptotic Value, Corresponding Julia Sets, IJBC 2010, Periodic Cycles