Scrambled sets for transitive maps

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F02%3A00000125" target="_blank" >RIV/47813059:19610/02:00000125 - 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

Scrambled sets for transitive maps

Original language description

We deal with two types of chaos: the well known chaos in the sense of Li and Yorke and $omega$-chaos which was introduced in [S. Li, {it Trans. Amer. Math. Soc.} 339 (1993)]. In this paper we prove that every bitransitive map $f in C(I,I)$ is conjugate to $g in C(I,I)$, which satisfies the following conditions, $1.$ there is a $c$-dense $omega$-scrambled set for $g$, $2.$ there is an extremely LY-scrambled set for $g$ with full Lebesgue measure, $3.$ every $omega$-scrambled set of $g$ has zero Lebesgue measure.

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/GP201%2F01%2FP134" target="_blank" >GP201/01/P134: Chaos in discrete dynamical systems</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2002

Confidentiality

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

Name of the periodical

Real Analysis Exchange

ISSN

ISSN0147-1937

e-ISSN

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Volume of the periodical

27

Issue of the periodical within the volume

2

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

8

Pages from-to

808-80

UT code for WoS article

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EID of the result in the Scopus database

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