Trojúhelníková zobrazení s uzavřenými množinami periodických bodů

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F06%3A%230000053" target="_blank" >RIV/47813059:19610/06:#0000053 - 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

Triangular maps with closed sets of periodic points

Popis výsledku v původním jazyce

In a recent paper we provided a characterization of triangular maps of the square, i.e., maps given by $F(x,y)=(f(x),g_x(y))$, satisfying condition (P1) that any chain recurrent point is periodic. For continuous maps of the interval, there is a list of 18 other conditions equivalent to (P1), including (P2) that there is no infinite $omega$-limit set, (P3) that the set of periodic points is closed and (P4) that any regularly recurrent point is periodic, for instance. We provide an almost complete classification among these conditions for triangular maps, improve a recent result given by C. Arteaga (in J. Math. Anal. Appl. 196 (1995)) and state an open problem concerning minimal sets of triangular maps. The mentioned open problem is related to the question whether some regularly recurrent point lies in the fibres over an $f$-minimal set possessing a regularly recurrent point. We answered this question in the positive for triangular maps with nondecre asing fiber maps.

Název v anglickém jazyce

Triangular maps with closed sets of periodic points

Popis výsledku anglicky

In a recent paper we provided a characterization of triangular maps of the square, i.e., maps given by $F(x,y)=(f(x),g_x(y))$, satisfying condition (P1) that any chain recurrent point is periodic. For continuous maps of the interval, there is a list of 18 other conditions equivalent to (P1), including (P2) that there is no infinite $omega$-limit set, (P3) that the set of periodic points is closed and (P4) that any regularly recurrent point is periodic, for instance. We provide an almost complete classification among these conditions for triangular maps, improve a recent result given by C. Arteaga (in J. Math. Anal. Appl. 196 (1995)) and state an open problem concerning minimal sets of triangular maps. The mentioned open problem is related to the question whether some regularly recurrent point lies in the fibres over an $f$-minimal set possessing a regularly recurrent point. We answered this question in the positive for triangular maps with nondecre asing fiber maps.

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

<a href="/cs/project/GA201%2F03%2F1153" target="_blank" >GA201/03/1153: Dynamické systémy II.</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2006

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

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Svazek periodika

319

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

302-314

Kód UT WoS článku

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EID výsledku v databázi Scopus

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