New exotic minimal sets from pseudo-suspensions of Cantor systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2401I39" target="_blank" >RIV/61988987:17610/23:A2401I39 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/abs/1609.09121" target="_blank" >https://arxiv.org/abs/1609.09121</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10884-021-10069-3" target="_blank" >10.1007/s10884-021-10069-3</a>
Alternative languages
Result language
angličtina
Original language name
New exotic minimal sets from pseudo-suspensions of Cantor systems
Original language description
We develop a technique, pseudo-suspension, that applies to invariant sets of homeomorphisms of a class of annulus homeomorphisms we describe, Handel–Anosov–Katok (HAK) homeomorphisms, that generalize the homeomorphism first described by Handel. Given a HAK homeomorphism and a homeomorphism of the Cantor set, the pseudo-suspension yields a homeomorphism of a new space that combines features of both of the original homeomorphisms. This allows us to answer a well known open question by providing examples of hereditarily indecomposable continua that admit homeomorphisms with positive finite entropy. Additionally, we show that such examples occur as minimal sets of volume preserving smooth diffeomorphisms of 4-dimensional manifolds.We construct an example of a minimal, weakly mixing and uniformly rigid homeomorphism of the pseudo-circle, and by our method we are also able to extend it to other one-dimensional hereditarily indecomposable continua, thereby producing the first examples of minimal, uniformly rigid and weakly mixing homeomorphisms in dimension 1. We also show that the examples we construct can be realized as invariant sets of smooth diffeomorphisms of a 4-manifold. Until now the only known examples of connected spaces that admit minimal, uniformly rigid and weakly mixing homeomorphisms were modifications of those given by Glasner and Maon in dimension at least 2.
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
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
J DYN DIFFER EQU
ISSN
1040-7294
e-ISSN
—
Volume of the periodical
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Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
1175-1201
UT code for WoS article
000693352800001
EID of the result in the Scopus database
2-s2.0-85114192644