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Article

Title: On some iteration semigroups (English)
Author: Brzdęk, Janusz
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 31
Issue: 1
Year: 1995
Pages: 37-42
Summary lang: English
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Category: math
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Summary: Let $F$ be a disjoint iteration semigroup of $C^n$ diffeomorphisms mapping a real open interval $I\ne \varnothing $ onto $I$. It is proved that if $F$ has a dense orbit possesing a subset of the second category with the Baire property, then $F=\lbrace f_t\:\,f_t(x)=f^{-1}(f(x)+t)\text{ for every }x\in I, t\in R\rbrace $ for some $C^n$ diffeomorphism $f$ of $I$ onto the set of all reals $R$. The paper generalizes some results of J.A.Baker and G.Blanton [3]. (English)
Keyword: iteration semigroup
Keyword: diffeomorphism
Keyword: ordered semigroup
Keyword: Baire property
MSC: 26A18
MSC: 39B12
MSC: 39B22
idZBL: Zbl 0834.39011
idMR: MR1342373
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Date available: 2008-06-06T21:27:48Z
Last updated: 2012-05-10
Stable URL: http://hdl.handle.net/10338.dmlcz/107522
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Reference: [2] Baker, J.: A note on iteration groups.Aequationes Math. 28 (1985), 129-131. Zbl 0582.26001, MR 0781217
Reference: [3] Baker, J., Blanton, G.: Iteration groups generated by $C^n$ functions.Arch. Math. (Brno) 18 (1982), 121-127. MR 0682099
Reference: [4] Blanton, G.: Smoothness in disjoint groups of real functions under composition.C.R.Math. Rep. Acad. Sci. Canada 5 (1983), 169-172. Zbl 0518.26003, MR 0713677
Reference: [5] Blanton, G.: Smoothness in disjoint groups of real functions under composition.Aequationes Math. 35 (1988), 1-16. Zbl 0702.26010, MR 0939617
Reference: [6] Fuchs, L.: Partially ordered algebraic systems.Pergamon Press, Oxford-London-New York-Paris, 1963. Zbl 0137.02001, MR 0171864
Reference: [7] Kominek, Z., Kuczma, M.: Therems of Berstein-Doetsch, Piccard and Mehdi and semilinear topology.Arch. Math. (Basel) 52 (1989), 595-602. MR 1007635
Reference: [8] Neuman, F.: Simultaneous solutions of a system of Abel equations and differential equations with several deviations.Czechoslovak Math. J. 32 (107) (1982), 488-494. Zbl 0524.34070, MR 0669790
Reference: [9] Oxtoby, J.: Measure and Category.Graduate Texts in Mathematics 2, Springer-Verlag, New York-Heidelberg-Berlin, 1971. Zbl 0217.09201, MR 0584443
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