AN ESCAPE CRITERION FOR THE COMPLEX POLYNOMIAL, WITH APPLICATIONS TO THE DEGREE-n BIFURCATION SET

Abstract

Let Pc(z) = zn + c be a complex polynomial with an integer n 2. We derive a criterion that the critical orbit of Pc escapes to infinity and investigate its applications to the degree-n bifurcation set. The intersection of the degree-n bifurcation set with the real line as well as with a typical symmetric axis is explicitly written as a function of n. A well-defined escape-time algorithm is also included for the improved construction of the degree-n bifurcation set.

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