On the system of the Abel equations on the plane

Zbigniew Leśniak

Published: 1995-09-29

Vol. 9 (1995)

On the system of the Abel equations on the plane

Zbigniew Leśniak

Abstract

We find all of continuous, homeomorphic and Ck solutions of the system of the Abel equations
ϕ(f(x)) = ϕ(x)+a
ϕ(g(x)) = ϕ(x)+b for x∈ℝ²,
where a,b are linearly independent vectors and f,g are commutable orientation preserving homeomorphisms of the plane onto itself satisfying some condition which is equivalent to the fact that there exists a homeomorphic solution of the system above.

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Leśniak, Z. (1995). On the system of the Abel equations on the plane. Annales Mathematicae Silesianae, 9, 105–122. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14211

Vol. 9 (1995)
Published: 1995-09-29

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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