{"title":"Local non-periodic order and diam-mean equicontinuity on cellular automata","authors":"Luguis de los Santos Baños, Felipe Garc'ia-Ramos","doi":"10.1080/14689367.2022.2106823","DOIUrl":null,"url":null,"abstract":"Diam-mean equicontinuity is a dynamical property that has been of use in the study of non-periodic order. Using some type of ‘local’ skew product between a shift and an odometer looking cellular automaton (CA), we will show that there exists an almost diam-mean equicontinuous CA that is not almost equicontinuous (and hence not almost locally periodic). Previously, we constructed a CA that is almost mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Mean equicontinuity and mean sensitivity on cellular automata, Ergodic Theory Dynam. Systems 41 (12) (2021), pp. 3704–3721] but not almost diam-mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Diameter mean equicontinuity and cellular automata, Proceedings of the 27th International Workshop on Cellular Automata and Discrete Complex Systems, arXiv:2106.09641, 2021].","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"666 - 683"},"PeriodicalIF":0.5000,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2022.2106823","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
Diam-mean equicontinuity is a dynamical property that has been of use in the study of non-periodic order. Using some type of ‘local’ skew product between a shift and an odometer looking cellular automaton (CA), we will show that there exists an almost diam-mean equicontinuous CA that is not almost equicontinuous (and hence not almost locally periodic). Previously, we constructed a CA that is almost mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Mean equicontinuity and mean sensitivity on cellular automata, Ergodic Theory Dynam. Systems 41 (12) (2021), pp. 3704–3721] but not almost diam-mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Diameter mean equicontinuity and cellular automata, Proceedings of the 27th International Workshop on Cellular Automata and Discrete Complex Systems, arXiv:2106.09641, 2021].
直径平均等连续性是一种动力学性质,在非周期序的研究中有着广泛的应用。使用移位和看起来像里程计的元胞自动机(CA)之间的某种类型的“局部”斜积,我们将证明存在一个几乎直径平均等连续的CA,它不是几乎等连续的(因此也不是几乎局部周期的)。以前,我们构造了一个几乎平均等连续的CA[L.D.I.S.Baños和F.García-Ramos,细胞自动机上的平均等连续性和平均灵敏度,遍历理论动态系统41(12)(2021),pp.3704–3721],但不是几乎直径平均等连续[L.D.is.Baños and F。García-Ramos,Diameter均值等连续性与细胞自动机,第27届细胞自动机与离散复杂系统国际研讨会论文集,arXiv:210609641021]。
期刊介绍:
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences