On iteration groups of singularity-free homeomorphisms of the plane - Zdun, Marek Cezary; Leśniak, Zbigniew (Annales Mathematicae Silesianae, 1994)
Let D be a simply connected region on the plane. We prove that a continuous iteration group of homeomorphisms {ft : t∈ℝ} defined on D is of the form ft(x) = ϕ-1(ϕ(x)+te1) for x∈D, t∈ℝ, where e1=(1,0) and ϕ is a homeomorphism mapping D onto ℝ, if and only if f1 is a singularity-free homeomorphism, i.e. f1 =: f has the property that for every Jordan domain B ⊂ D there exists an integer n0 such that B∩fn[B] = ⌀ for |n| > n0, n∈ℤ.