On some iteration semigroups
Archivum Mathematicum (1995)
- Volume: 031, Issue: 1, page 37-42
- ISSN: 0044-8753
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topBrzdęk, Janusz. "On some iteration semigroups." Archivum Mathematicum 031.1 (1995): 37-42. <http://eudml.org/doc/247688>.
@article{Brzdęk1995,
abstract = {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].},
author = {Brzdęk, Janusz},
journal = {Archivum Mathematicum},
keywords = {iteration semigroup; diffeomorphism; ordered semigroup; Baire property; homeomorphisms; diffeomorphisms; orbits; graphs; translation equation; iteration; Baire property; sets of second category},
language = {eng},
number = {1},
pages = {37-42},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On some iteration semigroups},
url = {http://eudml.org/doc/247688},
volume = {031},
year = {1995},
}
TY - JOUR
AU - Brzdęk, Janusz
TI - On some iteration semigroups
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 1
SP - 37
EP - 42
AB - 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].
LA - eng
KW - iteration semigroup; diffeomorphism; ordered semigroup; Baire property; homeomorphisms; diffeomorphisms; orbits; graphs; translation equation; iteration; Baire property; sets of second category
UR - http://eudml.org/doc/247688
ER -
References
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