About: The space of omega-limit sets of piecewise continuous maps of the interval

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	According to a well-known result, the collection of all omega-limit sets of a continuous map of the interval equipped with the Hausdorff metric is a compact metric space. In this paper, a similar result is proved for piecewise continuous maps with finitely many points of discontinuity, if the points of discontinuity are not periodic for any variant of the map. A variant of f is a map g coinciding with f at any point of continuity and being continuous from one side at any point of discontinuity. It is also shown that omega-limit sets of these maps are locally saturating, another property known for continuous maps. However, contrary to the situation for continuous maps, there are piecewise continuous maps having locally saturating sets which are not omega-limit sets. A condition implying that a locally saturating set is an omega-limit set is presented According to a well-known result, the collection of all omega-limit sets of a continuous map of the interval equipped with the Hausdorff metric is a compact metric space. In this paper, a similar result is proved for piecewise continuous maps with finitely many points of discontinuity, if the points of discontinuity are not periodic for any variant of the map. A variant of f is a map g coinciding with f at any point of continuity and being continuous from one side at any point of discontinuity. It is also shown that omega-limit sets of these maps are locally saturating, another property known for continuous maps. However, contrary to the situation for continuous maps, there are piecewise continuous maps having locally saturating sets which are not omega-limit sets. A condition implying that a locally saturating set is an omega-limit set is presented (en)
Title	The space of omega-limit sets of piecewise continuous maps of the interval The space of omega-limit sets of piecewise continuous maps of the interval (en)
skos:prefLabel	The space of omega-limit sets of piecewise continuous maps of the interval The space of omega-limit sets of piecewise continuous maps of the interval (en)
skos:notation	RIV/47813059:19610/10:#0000267!RIV10-MSM-19610___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	2-3
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Smítal, Jaroslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	288928
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/10:#0000267
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	omega-limit set; Hausdorff metric; piecewise continuous map; interval map; compactness; locally saturating set (en)
http://linked.open.../riv/klicoveSlovo	interval map Hausdorff metric compactness omega-limit set locally saturating set piecewise continuous map
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[6A9EA48D7611]
http://linked.open...i/riv/nazevZdroje	Journal of Difference Equations and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	16
http://linked.open...iv/tvurceVysledku	Smítal, Jaroslav Hofbauer, Franz Raith, Peter
http://linked.open...ain/vavai/riv/wos	000275127200012
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	1023-6198
number of pages	16 (xsd:int)
http://localhost/t...ganizacniJednotka	19610
is http://linked.open...avai/riv/vysledek of	The space of omega-limit sets of piecewise continuous maps of the interval The space of omega-limit sets of piecewise continuous maps of the interval The space of omega-limit sets of piecewise continuous maps of the interval

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