A zero topological entropy map for which periodic points are not a $G_delta$ set

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F02%3A00000093" target="_blank" >RIV/47813059:19610/02:00000093 - 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

A zero topological entropy map for which periodic points are not a $G_delta$ set

Original language description

We exhibit an example of a continuous map of the interval of type 2^infinity, and hence of zero topologicalentropy, for which the setof periodic points is not a G_delta set. This disproves a conjecture by Sharkovsky from 1965. Unfortunately, this conjecture has been incorrectly quoted as a true statement by other authors in many papers and books.

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

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2002

Confidentiality

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

Name of the periodical

Ergodic theory and dynamical systems

ISSN

ISSN0143-3857

e-ISSN

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Volume of the periodical

22

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

3

Pages from-to

947-949

UT code for WoS article

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EID of the result in the Scopus database

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