About: Irregular recurrence in compact metric spaces

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.sciencedirect.com/science/article/pii/S0960077913001240
Description	For a continuous map f : X -> X of a compact metric space, the set IR(f) of irregularly recurrent points is the set of points which are upper density recurrent, but not lower density recurrent. These notions are related to the structure of the measure center, but many problems still remain open. We solve some of them. The main result, based on examples by Obadalova and Smital [Obadalova L, Smltal J. Counterexamples to the open problem by Zhou and Feng on minimal center of attraction. Nonlinearity 2012;25:1443-9], shows that positive topological entropy supported by the center C-z of attraction of a point z is not related to the property that C-z is the support of an invariant measure generated by z. We also show that IR(f) is invariant with respect to standard operations, like f(IR(f)) = IR(f), or IR(f(m)) = IR(f) for m is an element of N. For a continuous map f : X -> X of a compact metric space, the set IR(f) of irregularly recurrent points is the set of points which are upper density recurrent, but not lower density recurrent. These notions are related to the structure of the measure center, but many problems still remain open. We solve some of them. The main result, based on examples by Obadalova and Smital [Obadalova L, Smltal J. Counterexamples to the open problem by Zhou and Feng on minimal center of attraction. Nonlinearity 2012;25:1443-9], shows that positive topological entropy supported by the center C-z of attraction of a point z is not related to the property that C-z is the support of an invariant measure generated by z. We also show that IR(f) is invariant with respect to standard operations, like f(IR(f)) = IR(f), or IR(f(m)) = IR(f) for m is an element of N. (en)
Title	Irregular recurrence in compact metric spaces Irregular recurrence in compact metric spaces (en)
skos:prefLabel	Irregular recurrence in compact metric spaces Irregular recurrence in compact metric spaces (en)
skos:notation	RIV/47813059:19610/13:#0000396!RIV14-MSM-19610___
http://linked.open...avai/predkladatel	Matematický ústav v Opavě
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	September 2013
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Obadalová, Lenka
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	81239
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/13:#0000396
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	recurrence; topological entropy; invariant measures; Banach density (en)
http://linked.open.../riv/klicoveSlovo	Banach density recurrence invariant measures topological entropy
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[872EFA7DE967]
http://linked.open...i/riv/nazevZdroje	Chaos, Solitons & Fractals
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	54
http://linked.open...iv/tvurceVysledku	Obadalová, Lenka
http://linked.open...ain/vavai/riv/wos	000324442600013
issn	0960-0779
number of pages	5 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.chaos.2013.06.010
http://localhost/t...ganizacniJednotka	19610

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