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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Nonlinearity

ISSN

09517715

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

April

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

25

Strana od-do

2534-2557

Kód UT WoS článku

000788766400001

EID výsledku v databázi Scopus

2-s2.0-85129990581