Periodic points and shadowing property for generic Lebesgue measure preserving interval maps

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA23029AK" target="_blank" >RIV/61988987:17610/22:A23029AK - isvavai.cz</a>

Result on the web

<a href="https://iopscience.iop.org/article/10.1088/1361-6544/ac62df/pdf" target="_blank" >https://iopscience.iop.org/article/10.1088/1361-6544/ac62df/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/ac62df" target="_blank" >10.1088/1361-6544/ac62df</a>

Result language

angličtina

Original language name

Periodic points and shadowing property for generic Lebesgue measure preserving interval maps

Original language description

In this article we study dynamical behaviour of generic Lebesgue measure- preserving interval maps. We show that for each k greater or equal than 1 the set of periodic points of period at least k is a Cantor set of Hausdorff dimension zero and of upper box dimension one. Moreover, we obtain analogous results also in the context of generic Lebesgue measure-preserving circle maps. Furthermore, building on the former results, we show that there is a dense collection of transitive Lebesgue measure-preserving interval maps whose periodic points have full Lebesgue measure and whose periodic points of period k have positive measure for each k greater of equal than 1. Finally, we show that the generic continuous maps of the inter- val which preserve the Lebesgue measure satisfy the shadowing and periodic shadowing property.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

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

Name of the periodical

Nonlinearity

ISSN

09517715

e-ISSN

—

Volume of the periodical

—

Issue of the periodical within the volume

April

Country of publishing house

GB - UNITED KINGDOM

Number of pages

25

Pages from-to

2534-2557

UT code for WoS article

000788766400001

EID of the result in the Scopus database

2-s2.0-85129990581