On the system of the Abel equations on the plane


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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Published : 1995-09-29

LeśniakZ. (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

Zbigniew Leśniak 
Instytut Matematyki, Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie  Poland

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