Geodesic
On some iteration semigroups
Archivum mathematicum, Tome 31 (1995) no. 1, pp. 37-42
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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].
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].
Classification : 26A18, 39B12, 39B22
Keywords: iteration semigroup; diffeomorphism; ordered semigroup; Baire property 
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Brzdęk, Janusz. On some iteration semigroups. Archivum mathematicum, Tome 31 (1995) no. 1, pp. 37-42. http://geodesic.mathdoc.fr/item/ARM_1995_31_1_a3/

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