Perturbations in the speiser class

摘要

In this paper we study perturbations of maps from a family of expanding entire functions from the Speiser class. Maps in this family, which we denoted by R, have the form f(a)(z) = Sigma(n)(j=0) aje((j-k)z) where 0 < k < n and a = (a(0),... ,a(n)) is an element of Cn+1 is a parameter. Using a known result of Eremenko and Lyubich about structural stability of such maps, perturbation theory (Kato-Rellich theorem) and research of Urbanski and Zdunik on perturbations in the exponential family, we shall prove that the Hausdorff dimension of the set of points in the Julia set having nonescaping orbits depends analytically on the parameter a is an element of Cn+1.