Area of Julia Sets of Holomorphic Self-Maps on C

It is a general problem to study the measure of Julia sets. There are a lot of resultsfor rational and entire functions. In this note, we describe the measure of Julia set for someholomorphic self-maps on C~*. We’ll prove that J(f) has positive area, where f: C~*→C~*,f(z)=z~m e~(P(z)+Q(1/2)),P(z) and Q(z) are monic polynomials of degree d, and m is an integer.