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Bounded ergodic constructions, disjointness, and weak limits of powers 有限的遍历结构，不连贯和弱的权力限制
Transactions of the Moscow Mathematical Society Pub Date : 2014-04-09 DOI: 10.1090/S0077-1554-2014-00214-4
V. Ryzhikov
{"title":"Bounded ergodic constructions, disjointness, and weak limits of powers","authors":"V. Ryzhikov","doi":"10.1090/S0077-1554-2014-00214-4","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00214-4","url":null,"abstract":"This paper is devoted to the disjointness property of powers of a totally ergodic bounded construction of rank 1 and some generalizations of this result. We look at applications to the problem when the Möbius function is independent of the sequence induced by a bounded construction. Interest in the subject matter of this paper is related to the following observation. Bounded constructions of rank 1, under the condition that all their nonzero powers are ergodic, have nontrivial weak limits of powers. This implies that the powers of the constructions are disjoint (in the sense of [1]) and, in view of the results in [2], this results in bounded constructions being independent of the Möbius function. Thus, the problem of disjointness of powers of transformations, which had previously been regarded by specialists as a problem within the framework of self-joining theory, has an interesting application. Sarnak’s well-known conjecture [3] states that a strictly ergodic homeomorphism S : X → X with zero topological entropy has the property","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"165-171"},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00214-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626884","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: 13
On problems concerning moment-angle complexes and polyhedral products 关于矩角配合物和多面体积的问题
Transactions of the Moscow Mathematical Society Pub Date : 2014-04-09 DOI: 10.1090/S0077-1554-2014-00215-6
A. Bahri, M. Bendersky, F. Cohen, S. Gitler
{"title":"On problems concerning moment-angle complexes and polyhedral products","authors":"A. Bahri, M. Bendersky, F. Cohen, S. Gitler","doi":"10.1090/S0077-1554-2014-00215-6","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00215-6","url":null,"abstract":". The main goal of this paper is to give a list of problems closely connected to moment-angle complexes, polyhedral products","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"203-216"},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00215-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626922","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
Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions 矩形图的旁路。琼斯猜想及相关问题的证明
Transactions of the Moscow Mathematical Society Pub Date : 2014-04-09 DOI: 10.1090/S0077-1554-2014-00210-7
I. Dynnikov, M. Prasolov
{"title":"Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions","authors":"I. Dynnikov, M. Prasolov","doi":"10.1090/S0077-1554-2014-00210-7","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00210-7","url":null,"abstract":"In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually independent in a sense. It is shown that a minimal rectangular diagram maximizes the Thurston-Bennequin number for the corresponding Legendrian links. Jones' conjecture about the invariance of the algebraic number of intersections of a minimal braid representing a fixed link type is proved. A new proof of the monotonic simplification theorem for the unknot is given.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"208 1","pages":"97-144"},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83584961","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: 42
Hill’s formula for -periodic trajectories of Lagrangian systems 拉格朗日系统-周期轨迹的希尔公式
Transactions of the Moscow Mathematical Society Pub Date : 2014-04-09 DOI: 10.1090/S0077-1554-2014-00213-2
M. Davletshin
{"title":"Hill’s formula for -periodic trajectories of Lagrangian systems","authors":"M. Davletshin","doi":"10.1090/S0077-1554-2014-00213-2","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00213-2","url":null,"abstract":"In this paper some results of a work by Bolotin and Treshchëv are generalized to the case of g-periodic trajectories of Lagrangian systems. Formulae connecting the characteristic polynomial of the monodromy matrix with the determinant of the Hessian of the action functional are obtained both for the discrete and continuous cases. Applications to the problem of stability of g-periodic trajectories are given. Hill’s formula can be used to study g-periodic orbits obtained by variational methods. §","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"65-96"},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00213-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626867","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: 3
Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2 1和2属曲线雅可比矩阵束上的几何微分方程
Transactions of the Moscow Mathematical Society Pub Date : 2014-04-09 DOI: 10.1090/S0077-1554-2014-00223-5
E. Yu. Netaĭ
{"title":"Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2","authors":"E. Yu. Netaĭ","doi":"10.1090/S0077-1554-2014-00223-5","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00223-5","url":null,"abstract":". We construct some differential equations describing the geometry of bundles of Jacobians of algebraic curves of genus 1 and 2. For an elliptic curve we produce differential equations on the coefficients of a cometric compatible with the Gauss–Manin connection of the universal bundle of Jacobians of elliptic curves. This cometric is defined in terms of a solution F of the linear system of differential equations","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"37 1","pages":"281-292"},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00223-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627103","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
On the algebra of Siegel modular forms of genus 2 关于格2的西格尔模形式的代数
Transactions of the Moscow Mathematical Society Pub Date : 2014-04-09 DOI: 10.1090/S0077-1554-2014-00217-X
E. Vinberg
{"title":"On the algebra of Siegel modular forms of genus 2","authors":"E. Vinberg","doi":"10.1090/S0077-1554-2014-00217-X","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00217-X","url":null,"abstract":"Using the methods of [11], we recover the old result of J. Igusa [3] saying that the algebra of even Siegel modular forms of genus 2 is freely generated by forms of weights 4, 6, 10, 12. We also determine the structure of the algebra of all Siegel modular forms of genus 2.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00217-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626973","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: 24
Periods of second kind differentials of (n,s)-curves (n,s)曲线的第二类微分周期
Transactions of the Moscow Mathematical Society Pub Date : 2013-05-14 DOI: 10.1090/S0077-1554-2014-00218-1
J. C. Eilbeck, K. Eilers, V. Enolski
{"title":"Periods of second kind differentials of (n,s)-curves","authors":"J. C. Eilbeck, K. Eilers, V. Enolski","doi":"10.1090/S0077-1554-2014-00218-1","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00218-1","url":null,"abstract":"The problem of generalisation of classical expressions for periods of second kind elliptic integrals in terms of theta-constants to higher genera is studied. In this context special class of algebraic curves – (n, s)-curves is considered. It is shown that required representations can be obtained by comparison of equivalent expressions for projective connection by Fay-Wirtinger and Klein-Weierstrass. The case of genus two hyperelliptic curve is considered as a principle example and a number of new Thomae and Rosenhain-type formulae are obtained. We anticipate that the analysis undertaken for genus two curve can be extended to higher genera hyperelliptic curve as well to other classes of (n, s) non-hyperelliptic curves.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"245-260"},"PeriodicalIF":0.0,"publicationDate":"2013-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00218-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627036","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
Unimodular triangulations of dilated 3-polytopes 扩张3-多面体的单模三角剖分
Transactions of the Moscow Mathematical Society Pub Date : 2013-04-26 DOI: 10.1090/S0077-1554-2014-00220-X
F. Santos, G. Ziegler
{"title":"Unimodular triangulations of dilated 3-polytopes","authors":"F. Santos, G. Ziegler","doi":"10.1090/S0077-1554-2014-00220-X","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00220-X","url":null,"abstract":"A seminal result in the theory of toric varieties, due to Knudsen, Mumford and Waterman (1973), asserts that for every lattice polytope $P$ there is a positive integer $k$ such that the dilated polytope $kP$ has a unimodular triangulation. In dimension 3, Kantor and Sarkaria (2003) have shown that $k=4$ works for every polytope. But this does not imply that every $k>4$ works as well. We here study the values of $k$ for which the result holds showing that: \u00001. It contains all composite numbers. \u00002. It is an additive semigroup. \u0000These two properties imply that the only values of $k$ that may not work (besides 1 and 2, which are known not to work) are $kin{3,5,7,11}$. With an ad-hoc construction we show that $k=7$ and $k=11$ also work, except in this case the triangulation cannot be guaranteed to be \"standard\" in the boundary. All in all, the only open cases are $k=3$ and $k=5$.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"293-311"},"PeriodicalIF":0.0,"publicationDate":"2013-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00220-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60627052","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: 19
Homotopy BV algebras in Poisson geometry 泊松几何中的同伦BV代数
Transactions of the Moscow Mathematical Society Pub Date : 2013-04-23 DOI: 10.1090/S0077-1554-2014-00216-8
Christopher Braun, A. Lazarev
{"title":"Homotopy BV algebras in Poisson geometry","authors":"Christopher Braun, A. Lazarev","doi":"10.1090/S0077-1554-2014-00216-8","DOIUrl":"https://doi.org/10.1090/S0077-1554-2014-00216-8","url":null,"abstract":"We define and study the degeneration property for $ mathrm {BV}_infty $ algebras and show that it implies that the underlying $ L_{infty }$ algebras are homotopy abelian. The proof is based on a generalisation of the well-known identity $ Delta (e^{xi })=e^{xi }Big (Delta (xi )+frac {1}{2}[xi ,xi ]Big )$ which holds in all BV algebras. As an application we show that the higher Koszul brackets on the cohomology of a manifold supplied with a generalised Poisson structure all vanish. - See more at: http://www.ams.org/journals/mosc/2013-74-00/S0077-1554-2014-00216-8/#sthash.pBIIcZKa.dpuf","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"217-227"},"PeriodicalIF":0.0,"publicationDate":"2013-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00216-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626935","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: 27
An asymptotic formula for polynomials orthonormal with respect to a varying weight 一个关于变权多项式标准正交的渐近公式
Transactions of the Moscow Mathematical Society Pub Date : 2013-03-21 DOI: 10.1090/S0077-1554-2013-00204-6
Trudy Moskov, Matem, Obw, A. Komlov, S. Suetin
{"title":"An asymptotic formula for polynomials orthonormal with respect to a varying weight","authors":"Trudy Moskov, Matem, Obw, A. Komlov, S. Suetin","doi":"10.1090/S0077-1554-2013-00204-6","DOIUrl":"https://doi.org/10.1090/S0077-1554-2013-00204-6","url":null,"abstract":". We obtain a strong asymptotic formula for the leading coefficient α n ( n ) of a degree n polynomial q n ( z ; n ) orthonormal on a system of intervals on the real line with respect to a varying weight. The weight depends on n as e − 2 nQ ( x ) , where Q ( x ) is a polynomial and corresponds to the “hard-edge case”. The formula in Theorem 1 is quite similar to Widom’s classical formula for a weight independent of n . In some sense, Widom’s formulas are still true for a varying weight and are thus universal. As a consequence of the asymptotic formula we have that α n ( n ) e − nw Q oscillates as n → ∞ and, in a typical case, fills an interval (here w Q is the equilibrium constant in the external field Q ).","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"73 1","pages":"139-159"},"PeriodicalIF":0.0,"publicationDate":"2013-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60626700","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: 9
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