On biaccessible points in the Julia sets of some rational functions

Abstract

We are interested in biaccessible points in the Julia sets of rational functions. D. Schleicher and S. Zakeri studied which points can be biaccessible in the Julia sets of quadratic polynomials with irrationally indifferent fixed points [SZ, Za]. In this paper, we consider the two polynomial families f_c(z) = z^d + c, g_θ(z) = e^2πiθz + z^d and the cubic rational family h_θ,a(z) = e^2πiθz²$\frac{z-a}{1-\bar{a}z}$.