On the boundary of an immediate attracting basin of a hyperbolic entire function

Abstract Let be a transcendental entire function of finite order which has an attracting periodic point of period at least 2. Suppose that the set of singularities of the inverse of is finite and contained in the component of the Fatou set that contains . Under an additional hypothesis, we show that the intersection of with the escaping set of has Hausdorff dimension 1. The additional hypothesis is satisfied for example if has the form with polynomials and and a constant . This generalizes a result of Barański, Karpińska, and Zdunik dealing with the case .