Renormalization in Lorenz maps – completely invariant sets and periodic orbits
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA25029QD" target="_blank" >RIV/61988987:17610/24:A25029QD - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0001870824004055" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0001870824004055</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2024.109890" target="_blank" >10.1016/j.aim.2024.109890</a>
Alternative languages
Result language
angličtina
Original language name
Renormalization in Lorenz maps – completely invariant sets and periodic orbits
Original language description
The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincarè maps in geometric models of well-known Lorenz attractor. Using both analytical and symbolic approaches, we study connections between periodic points, completely invariant sets and renormalizations. We show that some renormalizations may be connected with completely invariant sets while some others don't. We provide an algorithm to detect the renormalizations that can be recovered from completely invariant sets. Furthermore, we discuss the importance of distinguish one-side and double-side preimage. This way we provide a better insight into the structure of renormalizations in Lorenz maps. These relations remained unnoticed in the literature, therefore we are correcting some gaps existing in the literature, improving and completing to some extent the description of possible dynamics in this important field of study.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ADV MATH
ISSN
0001-8708
e-ISSN
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Volume of the periodical
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Issue of the periodical within the volume
November 2024
Country of publishing house
US - UNITED STATES
Number of pages
45
Pages from-to
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UT code for WoS article
001301379100001
EID of the result in the Scopus database
2-s2.0-85201680365