| bibtype |
J -
Journal Article
|
| ARLID |
0636737 |
| utime |
20250620112058.7 |
| mtime |
20250619235959.9 |
| SCOPUS |
85204494007 |
| WOS |
001309809400001 |
| DOI |
10.1017/etds.2024.43 |
| title
(primary) (eng) |
Minimal and proximal examples of d̄-stable and d̄-approachable shift spaces |
| specification |
| page_count |
31 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0252855 |
| ISSN |
0143-3857 |
| title
|
Ergodic Theory and Dynamical Systems |
| volume_id |
45 |
| volume |
2 (2025) |
| page_num |
396-426 |
| publisher |
| name |
Cambridge University Press |
|
|
| keyword |
specification property |
| keyword |
topological entropy |
| keyword |
shift space |
| keyword |
Poulsen simplex |
| keyword |
Besicovitch pseudometric |
| author
(primary) |
| ARLID |
cav_un_auth*0489436 |
| name1 |
Can |
| name2 |
M. E. |
| country |
PL |
|
| author
|
| ARLID |
cav_un_auth*0364287 |
| name1 |
Konieczny |
| name2 |
J. |
| country |
PL |
|
| author
|
| ARLID |
cav_un_auth*0219359 |
| name1 |
Kupsa |
| name2 |
Michal |
| institution |
UTIA-B |
| full_dept (cz) |
Stochastická informatika |
| full_dept |
Department of Stochastic Informatics |
| department (cz) |
SI |
| department |
SI |
| country |
CZ |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0364286 |
| name1 |
Kwietniak |
| name2 |
D. |
| country |
PL |
|
| source |
|
| source |
|
| cas_special |
| abstract
(eng) |
We study shift spaces over a finite alphabet that can be approximated by mixing shifts of finite type in the sense of (pseudo)metrics connected to Ornstein's (d) over bar metric ((d) over bar -approachable shift spaces). The class of (d) over bar -approachable shifts can beconsidered as a topological analog of measure-theoretical Bernoulli systems. The notionof (d) over bar -approachability, together with a closely connected notion of Itshows-shadowing, was introduced by Konieczny, Kupsa, and Kwietniak [Ergod. Th. & Dynam. Sys.43(3) (2023),943-970]. These notions were developed with the aim of significantly generalizing specification properties. Indeed, many popular variants of the specification property, includingthe classic one and the almost/weak specification property, ensure (d) over bar -approachability and (d) over bar -shadowing. Here, we study further properties and connections between (d) over bar -shadowing and (d) over bar -approachability. We prove that (d) over bar -shadowing implies (d) over bar -stability (a notion recently introduced by Tim Austin). We show that for surjective shift spaces with the (d) over bar -shadowingproperty the Hausdorff pseudodistance (d) over bar (H) between shift spaces induced by (d) over bar is the sameas the Hausdorff distance between their simplices of invariant measures with respect tothe Hausdorff distance induced by Ornstein's metric (d) over bar between measures. We prove thatwithout Itshows-shadowing this need not to be true (it is known that the former distance alwaysbounds the latter). We provide examples illustrating these results, including minimal examples and proximal examples of shift spaces with the (d) over bar -shadowing property. The existence of such shift spaces was announced in the earlier paper mentioned above. It shows that (d) over bar -shadowing indeed generalizes the specification property. |
| result_subspec |
WOS |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10101 |
| reportyear |
2026 |
| num_of_auth |
4 |
| inst_support |
RVO:67985556 |
| permalink |
https://hdl.handle.net/11104/0367702 |
| confidential |
S |
| mrcbC91 |
A |
| mrcbT16-e |
MATHEMATICS|MATHEMATICSAPPLIED |
| mrcbT16-j |
0.892 |
| mrcbT16-s |
1.005 |
| mrcbT16-D |
Q1 |
| mrcbT16-E |
Q1 |
| arlyear |
2025 |
| mrcbU14 |
85204494007 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
001309809400001 WOS |
| mrcbU63 |
cav_un_epca*0252855 Ergodic Theory and Dynamical Systems 0143-3857 1469-4417 Roč. 45 č. 2 2025 396 426 Cambridge University Press |
|