Triangular maps with the chain recurrent points periodic

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F03%3A00000115" target="_blank" >RIV/47813059:19610/03:00000115 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Triangular maps with the chain recurrent points periodic

Original language 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 $Itimes I$ 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~$g_x$.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F00%2F0859" target="_blank" >GA201/00/0859: Dynamical systems</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2003

Confidentiality

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

Name of the periodical

Acta Mathematica Universitatis Comenianae

ISSN

ISSN0862-9544

e-ISSN

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Volume of the periodical

72

Issue of the periodical within the volume

2

Country of publishing house

SK - SLOVAKIA

Number of pages

7

Pages from-to

245-25

UT code for WoS article

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EID of the result in the Scopus database

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