About: Triangular maps with the chain recurrent points periodic

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Forti and Paganoni [Grazer Math. Ber. {\bf 339} (1999), 125--140] found a triangular map $F(x,y)=(f(x),g_x (y))$ from $I\times I$ into itself for which closed set of~periodic points is a proper subset of the set of chain recurrent points. We asked whether there is a characterization of triangular maps for which every chain recurrent point is periodic. We answer this question in positive by showing that, for a triangular map with closed set of periodic points and any posi\-tive real~$\varepsilon$, every $\varepsilon$-chain from a chain recurrent point to itself may be represented as a finite union of $\varepsilon$-chains whose all points either are periodic or form a nontrivial $\varepsilon$-chain of some one-dimensional map~$g_x$. Forti and Paganoni [Grazer Math. Ber. {\bf 339} (1999), 125--140] found a triangular map $F(x,y)=(f(x),g_x (y))$ from $I\times I$ into itself for which closed set of~periodic points is a proper subset of the set of chain recurrent points. We asked whether there is a characterization of triangular maps for which every chain recurrent point is periodic. We answer this question in positive by showing that, for a triangular map with closed set of periodic points and any posi\-tive real~$\varepsilon$, every $\varepsilon$-chain from a chain recurrent point to itself may be represented as a finite union of $\varepsilon$-chains whose all points either are periodic or form a nontrivial $\varepsilon$-chain of some one-dimensional map~$g_x$. (en)
Title	Triangular maps with the chain recurrent points periodic Triangular maps with the chain recurrent points periodic (en)
skos:prefLabel	Triangular maps with the chain recurrent points periodic Triangular maps with the chain recurrent points periodic (en)
skos:notation	RIV/47813059:19610/03:00000115!RIV/2004/MSM/196104/N
http://linked.open.../vavai/riv/strany	245;25
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/00/0859), Z(MSM 192400002)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2004
http://linked.open...aciTvurceVysledku	Kupka, Jiří
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	631543
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/03:00000115
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Triangular maps; periodic points; chain recurrent poin (en)
http://linked.open.../riv/klicoveSlovo	Triangular maps periodic points chain recurrent poin
http://linked.open...odStatuVydavatele	SK - Slovenská republika
http://linked.open...ontrolniKodProRIV	[99BD263317CE]
http://linked.open...i/riv/nazevZdroje	Acta Mathematica Universitatis Comenianae
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...vavai/riv/projekt	Dynamical systems
http://linked.open...UplatneniVysledku	2003
http://linked.open...v/svazekPeriodika	72
http://linked.open...iv/tvurceVysledku	Kupka, Jiří
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20192400002
issn	0862-9544
number of pages	7 (xsd:int)
http://localhost/t...ganizacniJednotka	19610

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