Geodesic
On homeomorphic and diffeomorphic solutions of the Abel equation on the plane
Annales Polonici Mathematici, Tome 58 (1993) no. 1, pp. 7-18

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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.
DOI : 10.4064/ap-58-1-7-18
Keywords: functional Abel equation, free mapping

Zbigniew Leśniak 1

1 
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Zbigniew Leśniak. On homeomorphic and diffeomorphic solutions of the Abel equation on the plane. Annales Polonici Mathematici, Tome 58 (1993) no. 1, pp. 7-18. doi: 10.4064/ap-58-1-7-18

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