Pub Date : 2020-01-01DOI: 10.17323/1609-4514-2020-20-4-813-816
E. Petrova, S. Pirogov
{"title":"What is Time Reversal?","authors":"E. Petrova, S. Pirogov","doi":"10.17323/1609-4514-2020-20-4-813-816","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-4-813-816","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824827","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}
Pub Date : 2020-01-01DOI: 10.17323/1609-4514-2020-20-4-749-812
P. Major
{"title":"The Theory of Wiener–Itô Integrals in Vector Valued Gaussian Stationary Random Fields. Part I","authors":"P. Major","doi":"10.17323/1609-4514-2020-20-4-749-812","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-4-749-812","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824744","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}
Pub Date : 2020-01-01DOI: 10.17323/1609-4514-2020-20-4-641-644
S. Gusein-Zade, Y. Il'yashenko, K. Khanin, S. Shlosman, Y. Sinai, M. Tsfasman
{"title":"Roland Lvovich Dobrushin","authors":"S. Gusein-Zade, Y. Il'yashenko, K. Khanin, S. Shlosman, Y. Sinai, M. Tsfasman","doi":"10.17323/1609-4514-2020-20-4-641-644","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-4-641-644","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67825108","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}
Pub Date : 2020-01-01DOI: 10.17323/1609-4514-2020-20-4-817-818
Maxim Kazarian, Igor Moiseevich Krichever, S. K. Lando, Yu S Il'yashenko, Sergey Natanzon, Armen Sergeev, M. Tsfasman, Victor A. Vassiliev
{"title":"Sabir Gusein-Zade","authors":"Maxim Kazarian, Igor Moiseevich Krichever, S. K. Lando, Yu S Il'yashenko, Sergey Natanzon, Armen Sergeev, M. Tsfasman, Victor A. Vassiliev","doi":"10.17323/1609-4514-2020-20-4-817-818","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-4-817-818","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67825002","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}
Pub Date : 2019-11-28DOI: 10.17323/1609-4514-2022-22-4-595-611
E. Cabrera, Rogério Mol
Let $X$ be a germ of real analytic vector field at $({mathbb R}^{2},0)$ with an algebracally isolated singularity. We say that $X$ is a topological generalized curve if there are no topological saddle-nodes in its reduction of singularities. In this case, we prove that if either the order $nu_{0}(X)$ or the Milnor number $mu_{0}(X)$ is even, then $X$ has a formal separatrix, that is, a formal invariant curve at $0 in {mathbb R}^{2}$. This result is optimal, in the sense that these hypotheses do not assure the existence of a convergent separatrix.
设$X$为在$({mathbb R}^{2},0)$处具有代数孤立奇点的实解析向量场的胚芽。如果$X$的奇异性约简中不存在拓扑鞍节点，则称其为拓扑广义曲线。在这种情况下，我们证明了如果阶$nu_{0}(X)$或米尔诺数$mu_{0}(X)$是偶的，那么$X$有一个形式分离矩阵，即在$0 in {mathbb R}^{2}$处有一个形式不变曲线。这个结果是最优的，因为这些假设不能保证存在一个收敛的分离矩阵。
{"title":"Separatrices for Real Analytic Vector Fields in the Plane","authors":"E. Cabrera, Rogério Mol","doi":"10.17323/1609-4514-2022-22-4-595-611","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-4-595-611","url":null,"abstract":"Let $X$ be a germ of real analytic vector field at $({mathbb R}^{2},0)$ with an algebracally isolated singularity. We say that $X$ is a topological generalized curve if there are no topological saddle-nodes in its reduction of singularities. In this case, we prove that if either the order $nu_{0}(X)$ or the Milnor number $mu_{0}(X)$ is even, then $X$ has a formal separatrix, that is, a formal invariant curve at $0 in {mathbb R}^{2}$. This result is optimal, in the sense that these hypotheses do not assure the existence of a convergent separatrix.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46337396","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}
Pub Date : 2019-11-07DOI: 10.17323/1609-4514-2019-19-4-789-806
M. Tsfasman
{"title":"Serre's Theorem and Measures Corresponding to Abelian Varieties over Finite Fields","authors":"M. Tsfasman","doi":"10.17323/1609-4514-2019-19-4-789-806","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-4-789-806","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47261726","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}
Pub Date : 2019-11-07DOI: 10.17323/1609-4514-2019-19-4-695-707
L. Gogoladze, V. Tsagareishvili
{"title":"Differentiable Functions and General Orthonormal Systems","authors":"L. Gogoladze, V. Tsagareishvili","doi":"10.17323/1609-4514-2019-19-4-695-707","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-4-695-707","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43832914","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}
Pub Date : 2019-10-26DOI: 10.17323/1609-4514-2023-23-1-11-46
V. Araújo, J. Cerqueira
We prove that sectional-hyperbolic attracting sets for $C^1$ vector fields are robustly expansive (under an open technical condition of strong dissipative for higher codimensional cases). This extends known results of expansiveness for singular-hyperbolic attractors in $3$-flows even in this low dimensional setting. We deduce some converse results taking advantage of recent progress in the study of star vector fields: a robustly expansive non-singular vector field is uniformly hyperbolic; and a robustly transitive attractor is sectional-hyperbolic if, and only if, it is robustly expansive. In a low dimensional setting, we show that an attracting set of a $3$-flow is singular-hyperbolic if, and only if, it is robustly chaotic (robustly sensitive to initial conditions).
{"title":"On Robust Expansiveness for Sectional Hyperbolic Attracting Sets","authors":"V. Araújo, J. Cerqueira","doi":"10.17323/1609-4514-2023-23-1-11-46","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-1-11-46","url":null,"abstract":"We prove that sectional-hyperbolic attracting sets for $C^1$ vector fields are robustly expansive (under an open technical condition of strong dissipative for higher codimensional cases). This extends known results of expansiveness for singular-hyperbolic attractors in $3$-flows even in this low dimensional setting. We deduce some converse results taking advantage of recent progress in the study of star vector fields: a robustly expansive non-singular vector field is uniformly hyperbolic; and a robustly transitive attractor is sectional-hyperbolic if, and only if, it is robustly expansive. In a low dimensional setting, we show that an attracting set of a $3$-flow is singular-hyperbolic if, and only if, it is robustly chaotic (robustly sensitive to initial conditions).","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47606005","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}
Pub Date : 2019-09-09DOI: 10.17323/1609-4514-2021-21-1-31-42
Y. Bugeaud
Among other results, we establish, in a quantitative form, that any sufficiently large integer cannot simultaneously be divisible only by very small primes and have very few digits in its Zeckendorf representation.
{"title":"On the Zeckendorf Representation of Smooth Numbers","authors":"Y. Bugeaud","doi":"10.17323/1609-4514-2021-21-1-31-42","DOIUrl":"https://doi.org/10.17323/1609-4514-2021-21-1-31-42","url":null,"abstract":"Among other results, we establish, in a quantitative form, that any sufficiently large integer cannot simultaneously be divisible only by very small primes and have very few digits in its Zeckendorf representation.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48250941","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}
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：