Sharkovsky's program for the classification of triangular maps is almost completed

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F10%3A%230000282" target="_blank" >RIV/47813059:19610/10:#0000282 - 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

Sharkovsky's program for the classification of triangular maps is almost completed

Popis výsledku v původním jazyce

For a continuous map of the interval, there are more than 50 conditions characterizing zero topological entropy. Some are applicable to the class of triangular maps (x, y) bar right arrow (f(x), g(x)(y)) of the square, but only a few of them are equivalent in this more general setting. In 1989, A.N. Sharkovsky posed the problem of proving or disproving all possible implications between them. During last 20 years, 32 conditions were considered, and most of the work was done. Only 45 relations out of 992remained not clear. In this paper we give a survey of known results, provide two new examples disproving another 26 possible implications, and spell out the remaining 19 open problems; all but one concern distributional chaos.

Název v anglickém jazyce

Sharkovsky's program for the classification of triangular maps is almost completed

Popis výsledku anglicky

For a continuous map of the interval, there are more than 50 conditions characterizing zero topological entropy. Some are applicable to the class of triangular maps (x, y) bar right arrow (f(x), g(x)(y)) of the square, but only a few of them are equivalent in this more general setting. In 1989, A.N. Sharkovsky posed the problem of proving or disproving all possible implications between them. During last 20 years, 32 conditions were considered, and most of the work was done. Only 45 relations out of 992remained not clear. In this paper we give a survey of known results, provide two new examples disproving another 26 possible implications, and spell out the remaining 19 open problems; all but one concern distributional chaos.

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/GAP201%2F10%2F0887" target="_blank" >GAP201/10/0887: Diskrétní dynamické systémy</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

2010

Kód důvěrnosti údajů

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

Název periodika

Nonlinear Analysis: Theory, Methods & Applications

ISSN

0362-546X

e-ISSN

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Svazek periodika

73

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

7

Strana od-do

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Kód UT WoS článku

000280220200018

EID výsledku v databázi Scopus

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