PRIME ENDS DYNAMICS IN PARAMETRISED FAMILIES OF ROTATIONAL ATTRACTORS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F20%3AA2101VVP" target="_blank" >RIV/61988987:17610/20:A2101VVP - isvavai.cz</a>

Výsledek na webu

<a href="https://www.researchgate.net/publication/333700392_PRIME_ENDS_DYNAMICS_IN_PARAMETRISED_FAMILIES_OF_ROTATIONAL_ATTRACTORS" target="_blank" >https://www.researchgate.net/publication/333700392_PRIME_ENDS_DYNAMICS_IN_PARAMETRISED_FAMILIES_OF_ROTATIONAL_ATTRACTORS</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/jlms.12328" target="_blank" >10.1112/jlms.12328</a>

Jazyk výsledku

angličtina

Název v původním jazyce

PRIME ENDS DYNAMICS IN PARAMETRISED FAMILIES OF ROTATIONAL ATTRACTORS

Popis výsledku v původním jazyce

We provide several new examples in dynamics on the 2-sphere, with the emphasis on better understanding the induced boundary dynamics of invariant domains in parametrized families. First, motivated by a topological version of the Poincaré-Bendixson Theorem obtained recently by Koropecki and Passeggi, we show the existence of homeomorphisms of the 2-sphere with Lakes of Wada rotational attractors, with an arbitrarily large number of complementary domains, and with or without fixed points, that are arbitrarily close to the identity. This answers a question of Le Roux. Second, from reduced Arnold's family we construct a parametrised family of Birkhoff-like cofrontier attractors, where at least for uncountably many choices of the parameters, two distinct irrational prime ends rotation numbers are induced from the two complementary domains. This example complements the resolution of Walker's Conjecture by Koropecki, Le Calvez and Nassiri from 2015. Third, answering a question of Boyland, we show that there exists a non-transitive Birkhoff-like attracting cofrontier which is obtained from a BBM embedding of inverse limit of circles, such that the interior prime ends rotation number belongs to the interior of the rotation interval of the cofrontier dynamics. There exists another BBM embedding of the same attractor so that the two induced prime ends rotation numbers are exactly the two endpoints of the rotation interval.

Název v anglickém jazyce

PRIME ENDS DYNAMICS IN PARAMETRISED FAMILIES OF ROTATIONAL ATTRACTORS

Popis výsledku anglicky

We provide several new examples in dynamics on the 2-sphere, with the emphasis on better understanding the induced boundary dynamics of invariant domains in parametrized families. First, motivated by a topological version of the Poincaré-Bendixson Theorem obtained recently by Koropecki and Passeggi, we show the existence of homeomorphisms of the 2-sphere with Lakes of Wada rotational attractors, with an arbitrarily large number of complementary domains, and with or without fixed points, that are arbitrarily close to the identity. This answers a question of Le Roux. Second, from reduced Arnold's family we construct a parametrised family of Birkhoff-like cofrontier attractors, where at least for uncountably many choices of the parameters, two distinct irrational prime ends rotation numbers are induced from the two complementary domains. This example complements the resolution of Walker's Conjecture by Koropecki, Le Calvez and Nassiri from 2015. Third, answering a question of Boyland, we show that there exists a non-transitive Birkhoff-like attracting cofrontier which is obtained from a BBM embedding of inverse limit of circles, such that the interior prime ends rotation number belongs to the interior of the rotation interval of the cofrontier dynamics. There exists another BBM embedding of the same attractor so that the two induced prime ends rotation numbers are exactly the two endpoints of the rotation interval.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

J LOND MATH SOC (2)

ISSN

0024-6107

e-ISSN

—

Svazek periodika

102

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

23

Strana od-do

557-579

Kód UT WoS článku

000524314900001

EID výsledku v databázi Scopus

2-s2.0-85082970653