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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F10%3A%230000267" target="_blank" >RIV/47813059:19610/10:#0000267 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

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

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Difference Equations and Applications

ISSN

1023-6198

e-ISSN

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Svazek periodika

16

Číslo periodika v rámci svazku

2-3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

16

Strana od-do

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Kód UT WoS článku

000275127200012

EID výsledku v databázi Scopus

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