Periodic points and shadowing for generic Lebesgue measure-preserving interval maps
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F22%3A00365858" target="_blank" >RIV/68407700:21110/22:00365858 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1088/1361-6544/ac62df" target="_blank" >https://doi.org/10.1088/1361-6544/ac62df</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1361-6544/ac62df" target="_blank" >10.1088/1361-6544/ac62df</a>
Alternative languages
Result language
angličtina
Original language name
Periodic points and shadowing for generic Lebesgue measure-preserving interval maps
Original language description
In this article we study dynamical behavior of generic Lebesgue measure-preserving interval maps. We show that for each k = 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 = 1. Finally, we show that the generic continuous maps of the interval which preserve the Lebesgue measure satisfy the shadowing and periodic shadowing property.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinearity
ISSN
0951-7715
e-ISSN
1361-6544
Volume of the periodical
35
Issue of the periodical within the volume
5
Country of publishing house
GB - UNITED KINGDOM
Number of pages
24
Pages from-to
2534-2557
UT code for WoS article
000788766400001
EID of the result in the Scopus database
2-s2.0-85129990581