On iteration groups of singularity-free homeomorphisms of the plane

Marek Cezary Zdun; Zbigniew Leśniak

Published: 1994-09-30

Vol. 8 (1994)

On iteration groups of singularity-free homeomorphisms of the plane

Marek Cezary Zdun , Zbigniew Leśniak

Abstract

Let D be a simply connected region on the plane. We prove that a continuous iteration group of homeomorphisms {f^t : t∈ℝ} defined on D is of the form
f^t(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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Zdun, M. C., & Leśniak, Z. (1994). On iteration groups of singularity-free homeomorphisms of the plane. Annales Mathematicae Silesianae, 8, 203–210. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14235

References

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Marek Cezary Zdun

Affiliation:

Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland

Zbigniew Leśniak

Affiliation:

Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland

Vol. 8 (1994)
Published: 1994-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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