On iterative roots of homeomorphisms of the circle

• Autorzy: Zdun, M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we deal with the problem of existence and uniqueness of continuous iterative roots of homeomorphisms of the circle. Let F : [S^1 --> S^1] be a homeomorphism without periodic points. If the limit set of the orbit [F^k(z), k belongs to Z] equals [S^1], then F has exactly n iterative roots of n-th order. Otherwise F either has no iterative roots of n-th order or F has infinitely many iterative roots depending on an arbitrary function. In this case we determined all iterative roots of n-th order of F.

Słowa kluczowe

PL

orbita; pierwiastek iteracyjny; równanie funkcyjne

EN

functional equation; iterative root; lift; orbit; periodic points; rotation number

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 2
• Strony: 203--213
• Opis fizyczny: Bibliogr. 7 poz.,

Twórcy

autor

Zdun, M.

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

Bibliografia

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• [3] K. Ciepliński, On conjugacy of disjoint iteration groups on the unit circle, Ann. Math. Sil., to be published.
• [4] I. P. Cornfeld, S. V. F omi n, Y. G. Sinai, Ergodic theory, Grundlehren Math. Wiss. 245, Springer-Verlag, Berlin, Heidelberg, New York 1982.
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• [7] P. Walters, An introduction to ergodic theory, Springer-Verlag, New York, Heidelberg, Berlin 1982.