The meromorphic maps fλ(z) = λ(1−exp(−2z))−1, λ > 0, of the complex plane are thoroughly investigated. With each map fλ associated is its projection Fλ on the infinite cylinder Q. This map and the set Jr(Fλ) consisting of those points in the cylinder Q whose ω-limit set under Fλ is not contained in the set {0,−∞} will form the primary objects of our interest in this article. Let hλ = HD(Jr(Fλ))...
