Meromorphic functions that share a set with their derivatives

AbstractThere exists a set S with three elements such that if a meromorphic function f, having at most finitely many simple poles, shares the set S CM with its derivative f′, then f′≡f

A flower structure of backward flow invariant domains for semigroups

In this paper, we study conditions which ensure the existence of backward flow invariant domains for semigroups of holomorphic self-mappings of a simply connected domain D. More precisely, the problem is the following. Given a one-parameter semigroup S on D, find a simply connected subset Ω ⊂ D such that each element of S is an automorphism of Ω, in other words, such that S forms a one-parameter group on Ω. On the way to solving this problem, we prove an angle distortion theorem for starlike and spirallike functions with respect to interior and boundary points