About: A counterexample to statement concerning Lyapunov stability

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We exhibit an example of a continuous function $f$ of type $2^\infty$ on the unit interval such that $f$ is not stable in the sense of Ljapunov on the set ${\rm Per}(f)$ of its periodic points. This disproves a statement published in several books and papers, e.g., by V.V. Fedorenko, S. F. Kolyada, A. N. Sharkovsky, A. G. Sivak and J. Smítal. For completeness we also show that Ljapunov stability of $f$ on ${\rm Per}(f)$ implies that $f$ has zero topological entropy. We exhibit an example of a continuous function $f$ of type $2^\infty$ on the unit interval such that $f$ is not stable in the sense of Ljapunov on the set ${\rm Per}(f)$ of its periodic points. This disproves a statement published in several books and papers, e.g., by V.V. Fedorenko, S. F. Kolyada, A. N. Sharkovsky, A. G. Sivak and J. Smítal. For completeness we also show that Ljapunov stability of $f$ on ${\rm Per}(f)$ implies that $f$ has zero topological entropy. (en)
Title	A counterexample to statement concerning Lyapunov stability A counterexample to statement concerning Lyapunov stability (en)
skos:prefLabel	A counterexample to statement concerning Lyapunov stability A counterexample to statement concerning Lyapunov stability (en)
skos:notation	RIV/47813059:19610/01:00000064!RIV/2002/MSM/196102/N
http://linked.open.../vavai/riv/strany	265;268
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM 192400002)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2002
http://linked.open...aciTvurceVysledku	Augustová, Petra
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	672095
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/01:00000064
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	function of type 2^\infty; topological entropy; Ljapunov stability; periodic points (en)
http://linked.open.../riv/klicoveSlovo	periodic points topological entropy Ljapunov stability function of type 2^\infty
http://linked.open...odStatuVydavatele	SK - Slovenská republika
http://linked.open...ontrolniKodProRIV	[6915F16F1BC3]
http://linked.open...i/riv/nazevZdroje	Acta Mathematica Universitas Comeniane
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...ocetUcastnikuAkce	0 (xsd:int)
http://linked.open...nichUcastnikuAkce	0 (xsd:int)
http://linked.open...UplatneniVysledku	2001
http://linked.open...v/svazekPeriodika	70
http://linked.open...iv/tvurceVysledku	Šindelářová, Petra
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20192400002
issn	0862-9544
number of pages	4 (xsd:int)
http://localhost/t...ganizacniJednotka	19610

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