Journal of Modern Dynamics最新文献

{"title":"From invariance to self-similarity: The work of Michael Hochman on fractal dimension and its aftermath","authors":"H. Furstenberg","doi":"10.3934/jmd.2019027","DOIUrl":"https://doi.org/10.3934/jmd.2019027","url":null,"abstract":"M. Hochman's work on the dimension of self-similar sets has given impetus to resolving other questions regarding fractal dimension. We describe Hochman's approach and its influence on the subsequent resolution by P. Shmerkin of the conjecture on the dimension of the intersection of begin{document}$ times p $end{document} - and begin{document}$ times q $end{document} -Cantor sets.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70084938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The 2019 Michael Brin Prize in Dynamical Systems","authors":"T. Editors","doi":"10.3934/jmd.2019015","DOIUrl":"https://doi.org/10.3934/jmd.2019015","url":null,"abstract":"","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70084722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The work of Lewis Bowen on the entropy theory of non-amenable group actions","authors":"J. Thouvenot","doi":"10.3934/JMD.2019016","DOIUrl":"https://doi.org/10.3934/JMD.2019016","url":null,"abstract":"We present the achievements of Lewis Bowen, or, more precisely, his breakthrough works after which a theory started to develop. The focus will therefore be made here on the isomorphism problem for Bernoulli actions of countable non-amenable groups which he solved brilliantly in two remarkable papers. Here two invariants were introduced, which led to many developments.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70084774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost-prime times in horospherical flows on the space of lattices","authors":"Taylor J. McAdam","doi":"10.3934/jmd.2019022","DOIUrl":"https://doi.org/10.3934/jmd.2019022","url":null,"abstract":"An integer is called almost-prime if it has fewer than a fixed number of prime factors. In this paper, we study the asymptotic distribution of almost-prime entries in horospherical flows on begin{document}$ Gammabackslash {{rm{SL}}}_n(mathbb{R}) $end{document} , where begin{document}$ Gamma $end{document} is either begin{document}$ {{rm{SL}}}_n(mathbb{Z}) $end{document} or a cocompact lattice. In the cocompact case, we obtain a result that implies density for almost-primes in horospherical flows where the number of prime factors is independent of basepoint, and in the space of lattices we show the density of almost-primes in abelian horospherical orbits of points satisfying a certain Diophantine condition. Along the way we give an effective equidistribution result for arbitrary horospherical flows on the space of lattices, as well as an effective rate for the equidistribution of arithmetic progressions in abelian horospherical flows.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70084884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"William A. Veech's publications","authors":"T. Editors","doi":"10.3934/jmd.2019i","DOIUrl":"https://doi.org/10.3934/jmd.2019i","url":null,"abstract":"","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70084989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An infinite surface with the lattice property Ⅱ: Dynamics of pseudo-Anosovs","authors":"W. Patrick Hooper","doi":"10.3934/jmd.2019009","DOIUrl":"https://doi.org/10.3934/jmd.2019009","url":null,"abstract":"","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70084651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On manifolds admitting stable type III$_{textbf1}$ Anosov diffeomorphisms","authors":"Zemer Kosloff","doi":"10.3934/JMD.2018020","DOIUrl":"https://doi.org/10.3934/JMD.2018020","url":null,"abstract":"We prove that for every begin{document}$d≠3$end{document} there is an Anosov diffeomorphism of begin{document}$mathbb{T}^{d}$end{document} which is of stable Krieger type begin{document}${rm III}_1$end{document} (its Maharam extension is weakly mixing). This is done by a construction of stable type begin{document}${rm III}_1$end{document} Markov measures on the golden mean shift which can be smoothly realized as a begin{document}$C^{1}$end{document} Anosov diffeomorphism of begin{document}$mathbb{T}^2$end{document} via the construction in our earlier paper.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41998099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Roy Adler and the lasting impact of his work","authors":"B. Kitchens, B. Marcus, B. Weiss","doi":"10.3934/JMD.2018V","DOIUrl":"https://doi.org/10.3934/JMD.2018V","url":null,"abstract":"Roy Adler (1931–2016) earned his Ph.D. in 1961 from Yale University under the supervision of Shizuo Kakutani with a dissertation titled “On Some Algebraic Aspects of Measure Preserving Transformations.” His entire career was spent at the IBM Thomas J. Watson Research Center, with many short-term and longterm visits to universities. He was a fellow of the American Academy of Arts and Sciences, the American Mathematical Society, and the New York Academy of Arts and Sciences. He also served on the Board of Trustees of the American Mathematical Society. Among his seminal scientific achievements are the invention of topological entropy, the first applications of Markov partitions for dynamical systems and the application of symbolic dynamics to coding problems in hyperbolic geometry and information theory. These will be discussed in more detail later on. Roy’s interest in ergodic theory and symbolic dynamics led him to develop an algorithm to design codes to meet the constraints for data storage and transmission channels. A paper, including co-authors, Don Coppersmith and Martin Hassner, documenting these developments won the IEEE Information Theory Group 1985 Best Paper prize. IBM awarded Roy a Fourth Plateau Invention Achievement award, two IBM Research Outstanding Innovation awards, an Outstanding Technical Achievement award and the 2000 Research Patent Portfolio award. Roy was a contributor to more than 50 publications, in ergodic theory and symbolic dynamics, and 10 patents on coding, printing, spine modeling, x-ray data acquisition and cryptography. He was also a caring and inspiring mentor to several young mathematicians. An intellectual with a sharp and dry wit, his passions included great food, opera, fishing, good friends, and most of all his family. Roy was married to Audrey Wanner who passed away in 1990 and then to Judith Hershaft. He was a dedicated and adoring father to his two children, Caroline Kosaka and Michael Adler, his stepchildren and grandchildren. Probably Roy’s most important contribution to ergodic theory and topological dynamics was his introduction of topological entropy as the topological analogue of the measure-theoretic dynamical entropy that had been by defined by A. N. Kolmogorov [33] just a few years earlier. A version of topological entropy can be found in earlier work of W. Parry [36] and C. Shannon [42], but only for shifts of finite type. The definition given in Roy’s foundational paper","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46292656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A family of quaternionic monodromy groups of the Kontsevich–Zorich cocycle","authors":"Rodolfo Guti'errez-Romo","doi":"10.3934/jmd.2019008","DOIUrl":"https://doi.org/10.3934/jmd.2019008","url":null,"abstract":"For all begin{document}$ d $end{document} belonging to a density- begin{document}$ 1/8 $end{document} subset of the natural numbers, we give an example of a square-tiled surface conjecturally realizing the group begin{document}$ mathrm{SO}^*(2d) $end{document} in its standard representation as the Zariski-closure of a factor of its monodromy. We prove that this conjecture holds for the first elements of this subset, showing that the group begin{document}$ mathrm{SO}^*(2d) $end{document} is realizable for every begin{document}$ 11 leq d leq 299 $end{document} such that begin{document}$ d = 3 bmod 8 $end{document} , except possibly for begin{document}$ d = 35 $end{document} and begin{document}$ d = 203 $end{document} .","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42012383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The work of Mike Hochman on multidimensional symbolic dynamics and Borel dynamics","authors":"Mike Boyle","doi":"10.3934/jmd.2019026","DOIUrl":"https://doi.org/10.3934/jmd.2019026","url":null,"abstract":"This paper is based on my April 2018 talk at the Maryland-Penn State dynamics conference, on the occasion of Mike Hochman receiving the Brin Prize.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48273264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}