Renormalization in Lorenz maps – completely invariant sets and periodic orbits

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Renormalization in Lorenz maps – completely invariant sets and periodic orbits

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Renormalization in Lorenz maps – completely invariant sets and periodic orbits

Popis výsledku anglicky

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.

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

2024

Kód důvěrnosti údajů

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

Název periodika

ADV MATH

ISSN

0001-8708

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

November 2024

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

45

Strana od-do

—

Kód UT WoS článku

001301379100001

EID výsledku v databázi Scopus

2-s2.0-85201680365