Szczegóły publikacji
Opis bibliograficzny
New exotic minimal sets from pseudo-suspensions of cantor systems / Jan P. BOROŃSKI, Alex Clark, Piotr OPROCHA // Journal of Dynamics and Differential Equations ; ISSN 1040-7294. — 2023 — vol. 35 iss. 2, s. 1175–1201. — Bibliogr. s. 1200–1201, Abstr. — Publikacja dostępna online od: 2021-09-04. — J. P. Boroński, P. Oprocha - dod. afiliacja: National Supercomputing Centre IT4Innovations, Division of the University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, Ostrava, Czech Republic
Autorzy (3)
- AGHBoroński Jan
- Clark Alex
- AGHOprocha Piotr
Słowa kluczowe
Dane bibliometryczne
ID BaDAP | 148322 |
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Data dodania do BaDAP | 2023-09-27 |
Tekst źródłowy | URL |
DOI | 10.1007/s10884-021-10069-3 |
Rok publikacji | 2023 |
Typ publikacji | artykuł w czasopiśmie |
Otwarty dostęp | |
Creative Commons | |
Czasopismo/seria | Journal of Dynamics and Differential Equations |
Abstract
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.