RELATIVE INVARIANCE FOR MONOID ACTIONS

Let S be a topological monoid acting on the topological space M. Let J be a subset of M. Our purpose here is to study the subsets of M which correspond, under the action of S, to the relative (with respect to J) invariant control sets for control systems (see [4] section 3.3). The relation x y if y...

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Autor principal: BRAGA,CARLOS
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2001
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172001000300002
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spelling oai:scielo:S0716-091720010003000022002-07-15RELATIVE INVARIANCE FOR MONOID ACTIONSBRAGA,CARLOSLet S be a topological monoid acting on the topological space M. Let J be a subset of M. Our purpose here is to study the subsets of M which correspond, under the action of S, to the relative (with respect to J) invariant control sets for control systems (see [4] section 3.3). The relation x y if y 2 cl(Sx) and x 2 cl(Sy) is an equivalence relation and the classes with respect to this relation with nonempty interior in M are the control sets for the action of S. It is given conditions for the existence and uniqueness of relative invariant classes. As it was done for the control sets, we define an order in the classes and relate it to the relative invariant classes. We also show under certain condition that the relative invariant classes are relatively closed in Jinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.20 n.3 20012001-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172001000300002en10.4067/S0716-09172001000300002
institution Scielo Chile
collection Scielo Chile
language English
description Let S be a topological monoid acting on the topological space M. Let J be a subset of M. Our purpose here is to study the subsets of M which correspond, under the action of S, to the relative (with respect to J) invariant control sets for control systems (see [4] section 3.3). The relation x y if y 2 cl(Sx) and x 2 cl(Sy) is an equivalence relation and the classes with respect to this relation with nonempty interior in M are the control sets for the action of S. It is given conditions for the existence and uniqueness of relative invariant classes. As it was done for the control sets, we define an order in the classes and relate it to the relative invariant classes. We also show under certain condition that the relative invariant classes are relatively closed in J
author BRAGA,CARLOS
spellingShingle BRAGA,CARLOS
RELATIVE INVARIANCE FOR MONOID ACTIONS
author_facet BRAGA,CARLOS
author_sort BRAGA,CARLOS
title RELATIVE INVARIANCE FOR MONOID ACTIONS
title_short RELATIVE INVARIANCE FOR MONOID ACTIONS
title_full RELATIVE INVARIANCE FOR MONOID ACTIONS
title_fullStr RELATIVE INVARIANCE FOR MONOID ACTIONS
title_full_unstemmed RELATIVE INVARIANCE FOR MONOID ACTIONS
title_sort relative invariance for monoid actions
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2001
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172001000300002
work_keys_str_mv AT bragacarlos relativeinvarianceformonoidactions
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