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On some iteration semigroups

Janusz Brzdęk (1995)

Archivum Mathematicum

Let F be a disjoint iteration semigroup of C n diffeomorphisms mapping a real open interval I 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 = { f t f t ( x ) = f - 1 ( f ( x ) + t ) for every x I , t R } 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].

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