{"title":"Bratteli diagrams for bounded topological speedups","authors":"Drew D. Ash, A. Dykstra, M. LeMasurier","doi":"10.1080/14689367.2023.2170775","DOIUrl":null,"url":null,"abstract":"ABSTRACT A bounded topological speedup of a Cantor minimal system is a minimal system , where for some bounded function , or any system topologically conjugate to such an . Assuming the system is represented by a properly ordered Bratteli diagram , we provide a method for constructing a new, perfectly ordered Bratteli diagram that represents the sped-up system . The diagram relates back to in a manner that enables us to see how certain dynamical properties are preserved under speedup. As an application, in the case that is a substitution minimal system, we show how to use to write an explicit substitution rule that generates the sped-up system , answering an open question from [L. Alvin, D.D. Ash, and N.S. Ormes, Bounded topological speedups, Dyn. Syst. 33(2) (2018), pp. 303–331.].","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"38 1","pages":"249 - 267"},"PeriodicalIF":0.5000,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2023.2170775","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: 0
Abstract
ABSTRACT A bounded topological speedup of a Cantor minimal system is a minimal system , where for some bounded function , or any system topologically conjugate to such an . Assuming the system is represented by a properly ordered Bratteli diagram , we provide a method for constructing a new, perfectly ordered Bratteli diagram that represents the sped-up system . The diagram relates back to in a manner that enables us to see how certain dynamical properties are preserved under speedup. As an application, in the case that is a substitution minimal system, we show how to use to write an explicit substitution rule that generates the sped-up system , answering an open question from [L. Alvin, D.D. Ash, and N.S. Ormes, Bounded topological speedups, Dyn. Syst. 33(2) (2018), pp. 303–331.].
摘要:Cantor最小系统的有界拓扑加速是这样的最小系统，其中对于某个有界函数，或与这样的函数拓扑共轭的任何系统。假设系统由一个适当有序的Bratteli图表示，我们提供了一种构造一个新的、完全有序的Bratteli图来表示加速系统的方法。该图以一种使我们能够看到某些动态特性在加速下是如何保持的方式联系起来。作为一个应用程序，在替换最小系统的情况下，我们展示了如何使用编写显式替换规则来生成加速系统，回答了来自[L]的开放问题。Alvin, D.D. Ash和N.S. Ormes，有界拓扑加速，Dyn. system . 33(2) (2018)， pp. 303-331。
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
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