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Topological and Metric Recurrence for General Markov Chains 一般马尔可夫链的拓扑和度量递归
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-10-22 DOI: 10.17323/1609-4514-2019-19-1-37-50
M. Blank
{"title":"Topological and Metric Recurrence for General Markov Chains","authors":"M. Blank","doi":"10.17323/1609-4514-2019-19-1-37-50","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-1-37-50","url":null,"abstract":"Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent points. We show that under some mild technical assumptions the set of non recurrent points is of zero reference measure. Necessary and sufficient conditions for a reference measure $m$ (which needs not to be dynamically invariant) to satisfy this property are obtained. These results are new even in the purely deterministic setting.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42350129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Smoothness of Derived Categories of Algebras 代数派生范畴的光滑性
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-10-17 DOI: 10.17323/1609-4514-2020-2-277-309
A. Elagin, V. Lunts, Olaf M. Schnurer
{"title":"Smoothness of Derived Categories of Algebras","authors":"A. Elagin, V. Lunts, Olaf M. Schnurer","doi":"10.17323/1609-4514-2020-2-277-309","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-2-277-309","url":null,"abstract":"We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for any algebra over a perfect field that is finite over its center and whose center is finitely generated as an algebra. These results are deduced from a general sufficient criterion for smoothness.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45020400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Palais Leaf-Space Manifolds and Surfaces Carrying Holomorphic Flows Palais叶空间流形与携带全纯流的曲面
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-10-16 DOI: 10.17323/1609-4514-2019-19-2-275-305
A. Ferreira, J. Rebelo, H. Reis
{"title":"Palais Leaf-Space Manifolds and Surfaces Carrying Holomorphic Flows","authors":"A. Ferreira, J. Rebelo, H. Reis","doi":"10.17323/1609-4514-2019-19-2-275-305","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-2-275-305","url":null,"abstract":"Starting from some remarkable singularities of holomorphic vector fields, we construct (open) complex surfaces over which the singularities in question are realized by complete vector fields. Our constructions lead to manifolds and vector fields beyond the algebraic setting and provide examples of complete vector fields with some new dynamical phenomena.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48846880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the Finite Dimensionality of Integrable Deformations of Strictly Convex Integrable Billiard Tables 严格凸可积台球桌可积变形的有限维性
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-09-25 DOI: 10.17323/1609-4514-2019-19-2-307-327
Guan Huang, V. Kaloshin
{"title":"On the Finite Dimensionality of Integrable Deformations of Strictly Convex Integrable Billiard Tables","authors":"Guan Huang, V. Kaloshin","doi":"10.17323/1609-4514-2019-19-2-307-327","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-2-307-327","url":null,"abstract":"In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table $Omega_0$ preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through $Omega_0$.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45466716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A New Family of Elliptic Curves with Unbounded Rank 一类新的无界秩椭圆曲线
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-09-20 DOI: 10.17323/1609-4514-2020-2-343-374
Richard Griffon
{"title":"A New Family of Elliptic Curves with Unbounded Rank","authors":"Richard Griffon","doi":"10.17323/1609-4514-2020-2-343-374","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-2-343-374","url":null,"abstract":"Let $mathbb{F}_q$ be a finite field of odd characteristic and $K= mathbb{F}_q(t)$. For any integer $dgeq 2$ coprime to $q$, consider the elliptic curve $E_d$ over $K$ defined by $y^2=x(x^2+t^{2d} x-4t^{2d})$. We show that the rank of the Mordell--Weil group $E_d(K)$ is unbounded as $d$ varies. The curve $E_d$ satisfies the BSD conjecture, so that its rank equals the order of vanishing of its $L$-function at the central point. We provide an explicit expression for the $L$-function of $E_d$, and use it to study this order of vanishing in terms of $d$.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49356567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Congruences on Infinite Partition and Partial Brauer Monoids 关于无穷分划和部分Brauer单调的同余
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-09-19 DOI: 10.17323/1609-4514-2022-22-2-295-372
J. East, N. Ruškuc
{"title":"Congruences on Infinite Partition and Partial Brauer Monoids","authors":"J. East, N. Ruškuc","doi":"10.17323/1609-4514-2022-22-2-295-372","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-2-295-372","url":null,"abstract":"We give a complete description of the congruences on the partition monoid $P_X$ and the partial Brauer monoid $PB_X$, where $X$ is an arbitrary infinite set, and also of the lattices formed by all such congruences. Our results complement those from a recent article of East, Mitchell, Ruskuc and Torpey, which deals with the finite case. As a consequence of our classification result, we show that the congruence lattices of $P_X$ and $PB_X$ are isomorphic to each other, and are distributive and well quasi-ordered. We also calculate the smallest number of pairs of partitions required to generate any congruence; when this number is infinite, it depends on the cofinality of certain limit cardinals.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42773258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Bifurcations of the Polycycle “Tears of the Heart”: Multiple Numerical Invariants 多周期“心之泪”的分岔：多重数值不变量
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-08-22 DOI: 10.17323/1609-4514-2020-2-323-341
N. Goncharuk, Yury Kudryashov
{"title":"Bifurcations of the Polycycle “Tears of the Heart”: Multiple Numerical Invariants","authors":"N. Goncharuk, Yury Kudryashov","doi":"10.17323/1609-4514-2020-2-323-341","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-2-323-341","url":null,"abstract":"\"Tears of the heart\" is a hyperbolic polycycle formed by three separatrix connections of two saddles. It is met in generic 3-parameter families of planar vector fields. \u0000In [arXiv:1506.06797], it was discovered that generically, the bifurcation of a vector field with \"tears of the heart\" is structurally unstable. The authors proved that the classification of such bifurcations has a numerical invariant. \u0000In this article, we study the bifurcations of \"tears of the heart\" in more detail, and find out that the classification of such bifurcation may have arbitrarily many numerical invariants.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49333772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Integrability in Finite Terms and Actions of Lie Groups 有限项的可积性与李群的作用
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-08-20 DOI: 10.17323/1609-4514-2019-19-2-329-341
A. Khovanskii
{"title":"Integrability in Finite Terms and Actions of Lie Groups","authors":"A. Khovanskii","doi":"10.17323/1609-4514-2019-19-2-329-341","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-2-329-341","url":null,"abstract":"According to Liouville's Theorem, an indefinite integral of an elementary function is usually not an elementary function. In this notes, we discuss that statement and a proof of this result. The differential Galois group of the extension obtained by adjoining an integral does not determine whether the integral is an elementary function or not. Nevertheless, Liouville's Theorem can be proved using differential Galois groups. The first step towards such a proof was suggested by Abel. This step is related to algebraic extensions and their finite Galois groups. A significant part of this notes is dedicated to a second step, which deals with pure transcendent extensions and their Galois groups which are connected Lie groups. The idea of the proof goes back to J.Liouville and J.Ritt.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43871964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Elements of the q-Askey Scheme in the Algebra of Symmetric Functions 对称函数代数中q-Askey格式的元素
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-08-19 DOI: 10.17323/1609-4514-2020-20-4-645-694
Cesar Cuenca, G. Olshanski
{"title":"Elements of the q-Askey Scheme in the Algebra of Symmetric Functions","authors":"Cesar Cuenca, G. Olshanski","doi":"10.17323/1609-4514-2020-20-4-645-694","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-4-645-694","url":null,"abstract":"The classical q-hypergeometric orthogonal polynomials are assembled into a hierarchy called the q-Askey scheme. At the top of the hierarchy, there are two closely related families, the Askey-Wilson and q-Racah polynomials. As it is well known, their construction admits a generalization leading to remarkable orthogonal symmetric polynomials in several variables. \u0000We construct an analogue of the multivariable q-Racah polynomials in the algebra of symmetric functions. Next, we show that our q-Racah symmetric functions can be degenerated into the big q-Jacobi symmetric functions, introduced in a recent paper by the second author. The latter symmetric functions admit further degenerations leading to new symmetric functions, which are analogues of q-Meixner and Al-Salam--Carlitz polynomials. \u0000Each of the four families of symmetric functions (q-Racah, big q-Jacobi, q-Meixner, and Al-Salam--Carlitz) forms an orthogonal system of functions with respect to certain measure living on a space of infinite point configurations. The orthogonality measures of the four families are of independent interest. We show that they are linked by limit transitions which are consistent with the degenerations of the corresponding symmetric functions.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49459944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On Elliptic Modular Foliations, II 关于椭圆模叶，II
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2018-08-05 DOI: 10.17323/1609-4514-2022-22-1-103-120
H. Movasati
{"title":"On Elliptic Modular Foliations, II","authors":"H. Movasati","doi":"10.17323/1609-4514-2022-22-1-103-120","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-1-103-120","url":null,"abstract":"We give an example of a one dimensional foliation F of degree two in a Zariski open set of a four dimensional weighted projective space which has only an enumerable set of algebraic leaves. These are defined over rational numbers and are isomorphic to modular curves X0(d), d ∈ N minus cusp points. As a by-product we get new models for modular curves for which we slightly modify an argument due to J. V. Pereira and give closed formulas for elements in their defining ideals. The general belief has been that such formulas do not exist and the emphasis in the literature has been on introducing faster algorithms to compute equations for small values of d.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48691151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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