ArticleOriginal scientific text
Title
On homeomorphic and diffeomorphic solutions of the Abel equation on the plane
Authors 1
Affiliations
- Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, Poland
Abstract
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.
Keywords
functional Abel equation, free mapping
Bibliography
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Pages:
7-18
Main language of publication
English
Received
1990-08-01
Accepted
1992-03-16
Published
1993
Exact and natural sciences