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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