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Keywords:
iteration semigroup; diffeomorphism; ordered semigroup; Baire property
iteration semigroup; diffeomorphism; ordered semigroup; Baire property
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].
References:
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