| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2008-06-06T21:27:48Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107522 |
| . |
| Reference:
|
[1] Aczél, J.: Funktionskomposition, Iterationsgruppen und Gewebe.Arch. Math. (Basel) 17 (1966), 469-475. MR 0203624 |
| 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 |
| . |
