Given a finite alphabet $mathbb{A}$ and a primitive substitution $theta:mathbb{A}tomathbb{A}^lambda$ (of constant length $lambda$), let $(X_theta,S)$ denote the corresponding dynamical system, where $X_{theta}$ is the closure of the orbit via the left shift $S$ of a fixed point of the natural extension of $theta$ to a self-map of $mathbb{A}^{mathbb{Z}}$. The main result of the paper is that all continuous observables in $X_{theta}$ are orthogonal to any bounded, aperiodic, multiplicative function $mathbf{u}:mathbb{N}tomathbb{C}$, i.e. [ lim_{Ntoinfty}frac1Nsum_{nleq N}f(S^nx)mathbf{u}(n)=0] for all $fin C(X_{theta})$ and $xin X_{theta}$. In particular, each primitive automatic sequence, that is, a sequence read by a primitive finite automaton, is orthogonal to any bounded, aperiodic, multiplicative function.
{"title":"Automatic sequences are orthogonal to aperiodic multiplicative functions","authors":"M. Lema'nczyk, C. Mullner","doi":"10.3934/dcds.2020260","DOIUrl":"https://doi.org/10.3934/dcds.2020260","url":null,"abstract":"Given a finite alphabet $mathbb{A}$ and a primitive substitution $theta:mathbb{A}tomathbb{A}^lambda$ (of constant length $lambda$), let $(X_theta,S)$ denote the corresponding dynamical system, where $X_{theta}$ is the closure of the orbit via the left shift $S$ of a fixed point of the natural extension of $theta$ to a self-map of $mathbb{A}^{mathbb{Z}}$. The main result of the paper is that all continuous observables in $X_{theta}$ are orthogonal to any bounded, aperiodic, multiplicative function $mathbf{u}:mathbb{N}tomathbb{C}$, i.e. [ lim_{Ntoinfty}frac1Nsum_{nleq N}f(S^nx)mathbf{u}(n)=0] for all $fin C(X_{theta})$ and $xin X_{theta}$. In particular, each primitive automatic sequence, that is, a sequence read by a primitive finite automaton, is orthogonal to any bounded, aperiodic, multiplicative function.","PeriodicalId":335105,"journal":{"name":"2019-20 MATRIX Annals","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116979253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-62497-2_12
P. Ivanov, Jilin W. J. L. Wang, Xiyun Zhang, Bolun Chen
{"title":"The New Frontier of Network Physiology: Emerging Physiologic States in Health and Disease from Integrated Organ Network Interactions","authors":"P. Ivanov, Jilin W. J. L. Wang, Xiyun Zhang, Bolun Chen","doi":"10.1007/978-3-030-62497-2_12","DOIUrl":"https://doi.org/10.1007/978-3-030-62497-2_12","url":null,"abstract":"","PeriodicalId":335105,"journal":{"name":"2019-20 MATRIX Annals","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128488071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-62497-2_18
C. E. Wright, S. Abarzhi
{"title":"Effect of Adiabatic Index on Richtmyer-Meshkov Flows Induced by Strong Shocks","authors":"C. E. Wright, S. Abarzhi","doi":"10.1007/978-3-030-62497-2_18","DOIUrl":"https://doi.org/10.1007/978-3-030-62497-2_18","url":null,"abstract":"","PeriodicalId":335105,"journal":{"name":"2019-20 MATRIX Annals","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123843814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-62497-2_64
Nobu Kishimoto, Y. Tsutsumi
{"title":"Correction to: A priori bounds for the kinetic DNLS","authors":"Nobu Kishimoto, Y. Tsutsumi","doi":"10.1007/978-3-030-62497-2_64","DOIUrl":"https://doi.org/10.1007/978-3-030-62497-2_64","url":null,"abstract":"","PeriodicalId":335105,"journal":{"name":"2019-20 MATRIX Annals","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117283591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this contribution, we discuss the automorphism group, i.e., the centralizer of the shift action inside the group of self-homeomorphisms of a subshift, together with the extended symmetry group (the corresponding normalizer) of certain Zd subshifts with a hierarchical structure, like bijective substitutive subshifts and the Robinson tiling.
{"title":"Extended symmetry groups of multidimensional subshifts with hierarchical structure","authors":"Álvaro Bustos","doi":"10.3934/dcds.2020250","DOIUrl":"https://doi.org/10.3934/dcds.2020250","url":null,"abstract":"In this contribution, we discuss the automorphism group, i.e., the centralizer of the shift action inside the group of self-homeomorphisms of a subshift, together with the extended symmetry group (the corresponding normalizer) of certain Zd subshifts with a hierarchical structure, like bijective substitutive subshifts and the Robinson tiling.","PeriodicalId":335105,"journal":{"name":"2019-20 MATRIX Annals","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125537144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-62497-2_26
Mako Sato, Y. Fukumoto
{"title":"Influence of an oblique magnetic field on planar flame front instability","authors":"Mako Sato, Y. Fukumoto","doi":"10.1007/978-3-030-62497-2_26","DOIUrl":"https://doi.org/10.1007/978-3-030-62497-2_26","url":null,"abstract":"","PeriodicalId":335105,"journal":{"name":"2019-20 MATRIX Annals","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126917707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：