Extreme chaos and transitivity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F03%3A00000113" target="_blank" >RIV/47813059:19610/03:00000113 - 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

Extreme chaos and transitivity

Original language description

In the eighties, Misiurewicz, Bruckner and Hu provided examples of functions chaotic in the sense of Li and Yorke almost everywhere. In this paper we show that similar results are true for distributional chaos, introduced in [B. Schweizer and J. Smital,Trans. Amer. Math. Soc. 334 (1994), 737--754]. In fact, we show that any bitransitive continuous map of the interval is conjugate to a map uniformly distributionally chaotic almost everywhere. Using a result of A. M. Blokh we get as a consequence that for any map $f$ with positive topological entropy there is a $k$ such that $f^k$ is semiconjugate to a continuous map uniformly distributionally chaotic almost everywhere, and consequently, chaotic in the sense of Li and Yorke almost everywhere.

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

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

ISSN

ISSN0218-1274

e-ISSN

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Volume of the periodical

13

Issue of the periodical within the volume

7

Country of publishing house

SG - SINGAPORE

Number of pages

6

Pages from-to

1695-170

UT code for WoS article

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EID of the result in the Scopus database

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