On iteration groups of singularity-free homeomorphisms of the plane
Abstract
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.
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Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
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