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.
@article{bwmeta1.element.bwnjournal-article-apmv58z1p7bwm,
author = {Zbigniew Le\'sniak},
title = {On homeomorphic and diffeomorphic solutions of the Abel equation on the plane},
journal = {Annales Polonici Mathematici},
volume = {58},
year = {1993},
pages = {7-18},
zbl = {0787.39006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p7bwm}
}
Zbigniew Leśniak. On homeomorphic and diffeomorphic solutions of the Abel equation on the plane. Annales Polonici Mathematici, Tome 58 (1993) pp. 7-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p7bwm/
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