### On homeomorphic and diffeomorphic solutions of the Abel equation on the plane

Zbigniew Leśniak (1993)

Annales Polonici Mathematici

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We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.