Parameterized family of annular homeomorphisms with pseudo-circle attractors

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA2502KQW" target="_blank" >RIV/61988987:17610/24:A2502KQW - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039624003735?pes=vor&utm_source=scopus&getft_integrator=scopus" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039624003735?pes=vor&utm_source=scopus&getft_integrator=scopus</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2024.06.008" target="_blank" >10.1016/j.jde.2024.06.008</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parameterized family of annular homeomorphisms with pseudo-circle attractors

Popis výsledku v původním jazyce

In this paper we construct a paramaterized family of annular homeomorphisms with Birkhoff-like rotational attractors that vary continuously with the parameter, are all homeomorphic to the pseudo-circle, display interesting boundary dynamics and furthermore preserve the induced Lebesgue measure from the circle. Namely, in the constructed family of attractors the outer prime ends rotation number vary continuously with the parameter through the interval [0,1/2]. This, in particular, answers a question from [J. London Math. Soc. (2) {bf 102} (2020), 557--579]. To show main results of the paper we first prove a result of an independent interest, that Lebesgue-measure preserving circle maps generically satisfy the crookedness condition which implies that generically the inverse limits of Lebesgue measure-preserving circle maps are hereditarily indecomposable. For degree one circle maps, this implies that the generic inverse limit in this context is the R.H. Bing's pseudo-circle.

Název v anglickém jazyce

Parameterized family of annular homeomorphisms with pseudo-circle attractors

Popis výsledku anglicky

In this paper we construct a paramaterized family of annular homeomorphisms with Birkhoff-like rotational attractors that vary continuously with the parameter, are all homeomorphic to the pseudo-circle, display interesting boundary dynamics and furthermore preserve the induced Lebesgue measure from the circle. Namely, in the constructed family of attractors the outer prime ends rotation number vary continuously with the parameter through the interval [0,1/2]. This, in particular, answers a question from [J. London Math. Soc. (2) {bf 102} (2020), 557--579]. To show main results of the paper we first prove a result of an independent interest, that Lebesgue-measure preserving circle maps generically satisfy the crookedness condition which implies that generically the inverse limits of Lebesgue measure-preserving circle maps are hereditarily indecomposable. For degree one circle maps, this implies that the generic inverse limit in this context is the R.H. Bing's pseudo-circle.

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

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

—

Číslo periodika v rámci svazku

25 October 2024

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

102-132

Kód UT WoS článku

001360774100001

EID výsledku v databázi Scopus

2-s2.0-85196561502