Surgery and hyperbolic univalent Baker domains

Abstract

We call a star with n-arms a set of n univalent Baker domains (UBDs) {U-i}(i=1)(n), such that for all i, j = 1,..., n and i not equal j, (U) over bar (i) boolean AND (U) over bar (j) =. In this paper we prove that for any numbers u, a >= 1, s >= 0 and numbers alpha(1), alpha(2),..., alpha(s) >= 2, there exists an entire transcendental map with a attracting domains, s stars, each one with alpha(i) arms, i = 1,..., s and u UBDs not contained in a star. Also, we construct an entire transcendental map with a period two of UBDs {U, f(U)}, such that (U) over bar boolean AND (f) over bar((U) over bar) = epsilon.