Parametrized family of pseudo-arc attractors: Physical measures and prime end rotations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302A3Z" target="_blank" >RIV/61988987:17610/22:A2302A3Z - isvavai.cz</a>

Výsledek na webu

<a href="https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/plms.12448" target="_blank" >https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/plms.12448</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/plms.12448" target="_blank" >10.1112/plms.12448</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parametrized family of pseudo-arc attractors: Physical measures and prime end rotations

Popis výsledku v původním jazyce

The main goal of this paper is to study topological and measure-theoretic properties of an intriguing family of strange planar attractors. Building toward these results, we first show that any generic Lebesgue measure-preserving map f generates the pseudo-arc as inverse limit with f as a single bonding map. These maps can be realized as attractors of disc homeomorphisms in such a way that the attractors vary continuously (in Hausdorff distance on the disc) with the change of bonding map as a parameter. Furthermore, for generic Lebesgue measure-preserving maps f the background Oxtoby–Ulam measures induced by Lebesgue measure for f on the interval are physical on the disc and in addition there is a dense set of maps f defining a unique physical measure. Moreover, the family of physical measures on the attractors varies continuously in the weak* topology; that is, the parametrized family is statistically stable. We also find an arc in the generic Lebesgue measure-preserving set of maps and construct a family of disk homeomorphisms parametrized by this arc which induces a continuously varying family of pseudo-arc attractors with prime ends rotation numbers varying continuously in [0,1/2]. It follows that there are uncountably many dynamically non-equivalent embeddings of the pseudo-arc in this family of attractors.

Název v anglickém jazyce

Parametrized family of pseudo-arc attractors: Physical measures and prime end rotations

Popis výsledku anglicky

The main goal of this paper is to study topological and measure-theoretic properties of an intriguing family of strange planar attractors. Building toward these results, we first show that any generic Lebesgue measure-preserving map f generates the pseudo-arc as inverse limit with f as a single bonding map. These maps can be realized as attractors of disc homeomorphisms in such a way that the attractors vary continuously (in Hausdorff distance on the disc) with the change of bonding map as a parameter. Furthermore, for generic Lebesgue measure-preserving maps f the background Oxtoby–Ulam measures induced by Lebesgue measure for f on the interval are physical on the disc and in addition there is a dense set of maps f defining a unique physical measure. Moreover, the family of physical measures on the attractors varies continuously in the weak* topology; that is, the parametrized family is statistically stable. We also find an arc in the generic Lebesgue measure-preserving set of maps and construct a family of disk homeomorphisms parametrized by this arc which induces a continuously varying family of pseudo-arc attractors with prime ends rotation numbers varying continuously in [0,1/2]. It follows that there are uncountably many dynamically non-equivalent embeddings of the pseudo-arc in this family of attractors.

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

2022

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the London Mathematical Society

ISSN

00246115

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

40

Strana od-do

318-357

Kód UT WoS článku

000793741900001

EID výsledku v databázi Scopus

2-s2.0-85129797814