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

• Autorzy: Zbigniew Leśniak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

functional Abel equation; free mapping

Kategorie tematyczne

• 54H20: Topological dynamics
• 26A18: Iteration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 1
• Strony: 7-18

Daty

wydano

1993

otrzymano

1990-08-01

poprawiono

1992-03-16

poprawiono

1992-05-10

Twórcy

autor

Zbigniew Leśniak

• Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, Poland

Bibliografia

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• [2] S. A. Andrea, The plane is not compactly generated by a free mapping, Trans. Amer. Math. Soc. 151 (1970), 481-498.
• [3] R. Engelking and K. Sieklucki, Topology. A Geometric Approach, Sigma Ser. Pure Math. 4, Heldermann, Berlin 1992.
• [4] T. Homma and H. Terasaka, On the structure of the plane translation of Brouwer, Osaka Math. J. 5 (1953), 233-266.
• [5] M. Kuczma, On the Schröder equation, Rozprawy Mat. 34 (1963).
• [6] R. Sikorski, Advanced Calculus. Functions of Several Variables, Monograf. Mat. 52, PWN, Warszawa 1969.
• [7] M. C. Zdun, On continuous iteration groups of fixed-point free mapping in ℝ² space, in: Proc. European Conference on Iteration Theory, Batschuns 1989, World Scientific, Singapore 1991, 362-368.