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Dynamics: Topology and Numbers最新文献

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Dynamical zeta functions of Reidemeister type and representations spaces Reidemeister型的动态zeta函数及其表示空间
Dynamics: Topology and Numbers Pub Date : 2019-06-21 DOI: 10.1090/conm/744/14979
A. Fel’shtyn, M. Zietek
{"title":"Dynamical zeta functions of Reidemeister type\u0000 and representations spaces","authors":"A. Fel’shtyn, M. Zietek","doi":"10.1090/conm/744/14979","DOIUrl":"https://doi.org/10.1090/conm/744/14979","url":null,"abstract":"In this paper we continue to study the Reidemeister zeta function. We prove P'olya -- Carlson dichotomy between rationality and a natural boundary for analytic behavior of the Reidemeister zeta function for a large class of automorphisms of Abelian groups. We also study dynamical representation theory zeta functions counting numbers of fixed irreducible representations for iterations of an endomorphism. The rationality and functional equation for these zeta functions are proven for several classes of groups. We find a connection between these zeta functions and the Reidemeister torsions of the corresponding mapping tori. We also establish the connection between the Reidemeister zeta function and dynamical representation theory zeta functions under restriction of endomorphism to a subgroup and to a quotient group.","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130580862","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}
引用次数: 6
Invariant measures for Cantor dynamical systems 康托动力系统的不变测度
Dynamics: Topology and Numbers Pub Date : 2019-04-21 DOI: 10.1090/conm/744/14988
S. Bezuglyi, O. Karpel
{"title":"Invariant measures for Cantor dynamical\u0000 systems","authors":"S. Bezuglyi, O. Karpel","doi":"10.1090/conm/744/14988","DOIUrl":"https://doi.org/10.1090/conm/744/14988","url":null,"abstract":"This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a homeomorphism has either a unique ergodic invariant measure or finitely many such measures (finitely ergodic homeomorphisms). Since every Cantor dynamical system $(X,T)$ can be realized as a Vershik map acting on the path space of a Bratteli diagram, we use combinatorial methods developed in symbolic dynamics and Bratteli diagrams during the last decade to study the simplex of invariant measures.","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129040351","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}
引用次数: 6
Dynamical generation of parameter laminations 参数分层的动态生成
Dynamics: Topology and Numbers Pub Date : 2019-04-17 DOI: 10.1090/conm/744/14986
A. Blokh, L. Oversteegen, V. Timorin
{"title":"Dynamical generation of parameter\u0000 laminations","authors":"A. Blokh, L. Oversteegen, V. Timorin","doi":"10.1090/conm/744/14986","DOIUrl":"https://doi.org/10.1090/conm/744/14986","url":null,"abstract":"Local similarity between the Mandelbrot set and quadratic Julia sets manifests itself in a variety of ways. We discuss a combinatorial one, in the language of geodesic laminations. More precisely, we compare quadratic invariant laminations representing Julia sets with the so-called Quadratic Minor Lamination (QML) representing a locally connected model of the Mandelbrot set. Similarly to the construction of an invariant lamination by pullbacks of certain leaves, we describe how QML can be generated by properly understood pullbacks of certain minors. In particular, we show that the minors of all non-renormalizable quadratic laminations can be obtained by taking limits of \"pullbacks\" of minors from the main cardioid. This is the second, amended version of the paper, to appear in Contemporary Mathematics","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128659016","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}
引用次数: 0
Dynamically affine maps in positive characteristic 正特征的动态仿射映射
Dynamics: Topology and Numbers Pub Date : 2019-04-09 DOI: 10.1090/conm/744/14982
J. Byszewski, G. Cornelissen, M. Houben, L. V. D. Meijden
{"title":"Dynamically affine maps in positive\u0000 characteristic","authors":"J. Byszewski, G. Cornelissen, M. Houben, L. V. D. Meijden","doi":"10.1090/conm/744/14982","DOIUrl":"https://doi.org/10.1090/conm/744/14982","url":null,"abstract":"We study fixed points of iterates of dynamically affine maps (a generalisation of Latt`es maps) over algebraically closed fields of positive characteristic $p$. We present and study certain hypotheses that imply a dichotomy for the Artin-Mazur zeta function of the dynamical system: it is either rational or non-holonomic, depending on specific characteristics of the map. We also study the algebraicity of the so-called tame zeta function, the generating function for periodic points of order coprime to $p$. We then verify these hypotheses for dynamically affine maps on the projective line, generalising previous work of Bridy, and, in arbitrary dimension, for maps on Kummer varieties arising from multiplication by integers on abelian varieties.","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116565904","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}
引用次数: 1
The inhomogeneous Sprindžhuk conjecture over a local field of positive characteristic 正特征局部场上的非齐次Sprindžhuk猜想
Dynamics: Topology and Numbers Pub Date : 2019-03-18 DOI: 10.1090/conm/744/14928
Arijit Ganguly, Anish Ghosh
{"title":"The inhomogeneous Sprindžhuk conjecture over\u0000 a local field of positive characteristic","authors":"Arijit Ganguly, Anish Ghosh","doi":"10.1090/conm/744/14928","DOIUrl":"https://doi.org/10.1090/conm/744/14928","url":null,"abstract":"We prove a strengthened version of the inhomogeneous Sprindzhuk conjecture in metric Diophantine approximation, over a local field of positive characteristic. The main tool is the transference principle of Beresnevich and Velani coupled with earlier work of the second named author who proved the standard, i.e. homogeneous version.","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127129121","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}
引用次数: 2
On weak rigidity and weakly mixing enveloping semigroups 关于弱刚性和弱混合包络半群
Dynamics: Topology and Numbers Pub Date : 2017-11-08 DOI: 10.1090/conm/744/14985
E. Akin, E. Glasner, B. Weiss
{"title":"On weak rigidity and weakly mixing enveloping\u0000 semigroups","authors":"E. Akin, E. Glasner, B. Weiss","doi":"10.1090/conm/744/14985","DOIUrl":"https://doi.org/10.1090/conm/744/14985","url":null,"abstract":"The question we deal with here, which was presented to us by Joe Auslander and Anima Nagar, is whether there is a nontrivial cascade (X,T) whose enveloping semigroup, as a dynamical system, is topologically weakly mixing (WM). After an introductory section recalling some definitions and classic results, we establish some necessary conditions for this to happen, and in the final section we show, using Ratner's theory, that the enveloping semigroup of the `time one map' of a classical horocycle flow is weakly mixing.","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126452283","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}
引用次数: 1
Periods of abelian differentials and dynamics 阿贝尔微分和动力学的周期
Dynamics: Topology and Numbers Pub Date : 2017-10-30 DOI: 10.1090/conm/744/14989
M. Kapovich
{"title":"Periods of abelian differentials and\u0000 dynamics","authors":"M. Kapovich","doi":"10.1090/conm/744/14989","DOIUrl":"https://doi.org/10.1090/conm/744/14989","url":null,"abstract":"Given a closed oriented surface S we describe those cohomology classes which appear as the period characters of abelian differentials for some choice of complex structure on S consistent with the orientation. The proof is based upon Ratner's solution of Raghunathan's conjecture.","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116915211","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}
引用次数: 15
Rigorous dimension estimates for Cantor sets arising in Zaremba theory Zaremba理论中Cantor集的严格维数估计
Dynamics: Topology and Numbers Pub Date : 1900-01-01 DOI: 10.1090/conm/744/14980
O. Jenkinson, M. Pollicott
{"title":"Rigorous dimension estimates for Cantor sets\u0000 arising in Zaremba theory","authors":"O. Jenkinson, M. Pollicott","doi":"10.1090/conm/744/14980","DOIUrl":"https://doi.org/10.1090/conm/744/14980","url":null,"abstract":"We address the question of the accuracy of bounds used in the study of Zaremba’s conjecture. Specifically, we establish rigorous estimates on the Hausdorff dimension of certain Cantor sets which arise in the analysis of Zaremba’s conjecture in [5, 18, 19, 23].","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"36 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":"130316816","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}
引用次数: 6
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