The Banach contraction mapping principle and cohomology
Commentationes Mathematicae Universitatis Carolinae (2000)
- Volume: 41, Issue: 3, page 605-610
- ISSN: 0010-2628
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topJanoš, Ludvík. "The Banach contraction mapping principle and cohomology." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 605-610. <http://eudml.org/doc/22513>.
@article{Janoš2000,
abstract = {By a dynamical system $(X,T)$ we mean the action of the semigroup $(\mathbb \{Z\}^+,+)$ on a metrizable topological space $X$ induced by a continuous selfmap $T:X\rightarrow X$. Let $M(X)$ denote the set of all compatible metrics on the space $X$. Our main objective is to show that a selfmap $T$ of a compact space $X$ is a Banach contraction relative to some $d_1\in M(X)$ if and only if there exists some $d_2\in M(X)$ which, regarded as a $1$-cocycle of the system $(X,T)\times (X,T)$, is a coboundary.},
author = {Janoš, Ludvík},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$B$-system; $E$-system},
language = {eng},
number = {3},
pages = {605-610},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The Banach contraction mapping principle and cohomology},
url = {http://eudml.org/doc/22513},
volume = {41},
year = {2000},
}
TY - JOUR
AU - Janoš, Ludvík
TI - The Banach contraction mapping principle and cohomology
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 3
SP - 605
EP - 610
AB - By a dynamical system $(X,T)$ we mean the action of the semigroup $(\mathbb {Z}^+,+)$ on a metrizable topological space $X$ induced by a continuous selfmap $T:X\rightarrow X$. Let $M(X)$ denote the set of all compatible metrics on the space $X$. Our main objective is to show that a selfmap $T$ of a compact space $X$ is a Banach contraction relative to some $d_1\in M(X)$ if and only if there exists some $d_2\in M(X)$ which, regarded as a $1$-cocycle of the system $(X,T)\times (X,T)$, is a coboundary.
LA - eng
KW - $B$-system; $E$-system
UR - http://eudml.org/doc/22513
ER -
References
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