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Russian Journal of Mathematical Physics最新文献

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Bifurcations of Magnetic Geodesic Flows on Surfaces of Revolution 旋转表面上磁测地线流的分岔
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600084
I.F. Kobtsev, E.A. Kudryavtseva
{"title":"Bifurcations of Magnetic Geodesic Flows on Surfaces of Revolution","authors":"I.F. Kobtsev,&nbsp;E.A. Kudryavtseva","doi":"10.1134/S1061920825600084","DOIUrl":"10.1134/S1061920825600084","url":null,"abstract":"<p> We study magnetic geodesic flows invariant under rotations on the 2-sphere. The dynamical system is given by a generic pair of functions <span>((f,Lambda))</span> in one variable. The topology of the Liouville fibration of the given integrable system near its singular orbits and singular fibers is described. The types of these singularities are computed. The topology of the Liouville fibration on regular 3-dimensional isoenergy manifolds is described by computing the Fomenko–Zieschang invariant. All possible bifurcation diagrams of the momentum mappings of such integrable systems are described. It is shown that the bifurcation diagram consists of two curves in the <span>((h,k))</span>-plane. One of these curves is a line segment <span>(h=0)</span>, and the other lies in the half-plane <span>(hge0)</span> and can be obtained from the curve <span>((a:-1:k) = (f:Lambda:1)^*)</span> projectively dual to the curve <span>((f:Lambda:1))</span> by the transformation <span>((a:-1:k)mapsto(a^2/2,k)=(h,k))</span>. </p><p> <b> DOI</b> 10.1134/S1061920825600084 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"65 - 96"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ky Fan Theorem for Sphere Bundles 球束的Ky范定理
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600138
G. Panina, R. Živaljević
{"title":"Ky Fan Theorem for Sphere Bundles","authors":"G. Panina,&nbsp;R. Živaljević","doi":"10.1134/S1061920825600138","DOIUrl":"10.1134/S1061920825600138","url":null,"abstract":"<p> The classical Ky Fan theorem is a combinatorial equivalent of the Borsuk–Ulam theorem. It is a generalization and extension of Tucker’s lemma and, just like its predecessor, it pinpoints important properties of antipodal colorings of vertices of a triangulated sphere <span>(S^n)</span>. Here we describe generalizations of Ky Fan theorem for the case when the sphere is replaced by the total space of a triangulated sphere bundle. </p><p> <b> DOI</b> 10.1134/S1061920825600138 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"141 - 149"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normal Subgroups Related to a One-Dimensional Pure Pseudorepresentation of a Group 与群的一维纯伪表示相关的正规子群
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825010133
A. I. Shtern
{"title":"Normal Subgroups Related to a One-Dimensional Pure Pseudorepresentation of a Group","authors":"A. I. Shtern","doi":"10.1134/S1061920825010133","DOIUrl":"10.1134/S1061920825010133","url":null,"abstract":"<p> By analogy with the normal subgroups related to pseudocharacters on groups, we introduce and study the properties of two normal subgroups of a group related to a one-dimensional pure pseudorepresentation on the group. </p><p> <b> DOI</b> 10.1134/S1061920825010133 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"185 - 188"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Fractional-Linear Integrals of Geodesics on Surfaces 曲面上测地线的分数-线性积分
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920824601836
B. Kruglikov
{"title":"On Fractional-Linear Integrals of Geodesics on Surfaces","authors":"B. Kruglikov","doi":"10.1134/S1061920824601836","DOIUrl":"10.1134/S1061920824601836","url":null,"abstract":"<p> In this note, we give a criterion for the existence of a fractional-linear integral for a geodesic flow on a Riemannian surface and explain that, modulo the Möbius transformations, the moduli space of such local integrals (if nonempty) is either the two-dimensional projective plane or a finite number of points. We also consider explicit examples and discuss a relation of such rational integrals to Killing vectors. </p><p> <b> DOI</b> 10.1134/S1061920824601836 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"97 - 104"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Suspensions over Cartesian Products of Rough Transformations of the Circle 圆的粗糙变换的笛卡尔积上的悬架
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920824601794
E. Nozdrinova, O. Pochinka, V. Shmukler, S. Zinina
{"title":"On Suspensions over Cartesian Products of Rough Transformations of the Circle","authors":"E. Nozdrinova,&nbsp;O. Pochinka,&nbsp;V. Shmukler,&nbsp;S. Zinina","doi":"10.1134/S1061920824601794","DOIUrl":"10.1134/S1061920824601794","url":null,"abstract":"<p> One of the constructions for obtaining flows on a manifold is the construction of a suspension over a diffeomorphism. S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. The converse is not true in the general case. A classic illustration of this fact are examples of nonconjugate diffeomorphisms of a circle whose suspensions are equivalent. In this paper, we establish relations between the invariants of topological conjugacy of Cartesian products of rough transformations of a circle and the invariants of topological equivalence of suspensions over them. </p><p> <b> DOI</b> 10.1134/S1061920824601794 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"129 - 140"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Index of Inönü–Wigner Contractions of Semisimple Lie Algebras 半单李代数的Inönü-Wigner缩约指标
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600199
D.A. Timashev
{"title":"Index of Inönü–Wigner Contractions of Semisimple Lie Algebras","authors":"D.A. Timashev","doi":"10.1134/S1061920825600199","DOIUrl":"10.1134/S1061920825600199","url":null,"abstract":"<p> We give an explicit formula for the index of a Lie algebra of the shape <span>( {mathfrak{g}} _0= {mathfrak{h}} oplus( {mathfrak{g}} / {mathfrak{h}} )^{ text{ab} })</span>, where <span>( {mathfrak{g}} )</span> is a semisimple Lie algebra, <span>( {mathfrak{h}} )</span> is a subalgebra in <span>( {mathfrak{g}} )</span> regarded as a subalgebra in <span>( {mathfrak{g}} _0)</span>, and <span>(( {mathfrak{g}} / {mathfrak{h}} )^{ text{ab} })</span> is an <span>( {mathfrak{h}} )</span>-module <span>( {mathfrak{g}} / {mathfrak{h}} )</span> regarded as an Abelian ideal of <span>( {mathfrak{g}} _0)</span>. This formula has applications to Poisson commutative subalgebras in the symmetric algebra <span>( operatorname{S} ( {mathfrak{g}} ))</span> and to completely integrable systems. </p><p> <b> DOI</b> 10.1134/S1061920825600199 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"189 - 195"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient Semiclassical Asymptotics with Simple Caustics in a Boundary Value Problem 边值问题中具有简单焦散的有效半经典渐近性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600072
S.Yu. Dobrokhotov, V.E. Nazaikinskiih, A.V. Tsvetkova, A.V. Turin
{"title":"Efficient Semiclassical Asymptotics with Simple Caustics in a Boundary Value Problem","authors":"S.Yu. Dobrokhotov,&nbsp;V.E. Nazaikinskiih,&nbsp;A.V. Tsvetkova,&nbsp;A.V. Turin","doi":"10.1134/S1061920825600072","DOIUrl":"10.1134/S1061920825600072","url":null,"abstract":"<p> In this paper we continue to develop the approach to constructing global uniform asymptotics of solutions of (pseudo)differential problems in terms of special functions based on the theory of the Maslov canonical operator. In particular, we show that if the corresponding Lagrangian manifold has a fold-type singularity, then the canonical operator on it is represented via the Airy function Ai and its derivative of complex arguments. This approach is illustrated by a known problem about construction of asymptotic eigenfunctions of the Laplace operator in an elliptic domain with Dirichlet boundary conditions. </p><p> <b> DOI</b> 10.1134/S1061920825600072 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"28 - 43"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Icosahedron in Birational Geometry 几何中的二十面体
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920824601800
Yu. Prokhorov
{"title":"Icosahedron in Birational Geometry","authors":"Yu. Prokhorov","doi":"10.1134/S1061920824601800","DOIUrl":"10.1134/S1061920824601800","url":null,"abstract":"<p> We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions. </p><p> <b> DOI</b> 10.1134/S1061920824601800 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"160 - 184"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conjugation Equation for Quaternionic Conjugation Spaces 四元数共轭空间的共轭方程
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600096
A. Kryazhev, D. Kuznetsov, Th. Popelensky
{"title":"Conjugation Equation for Quaternionic Conjugation Spaces","authors":"A. Kryazhev,&nbsp;D. Kuznetsov,&nbsp;Th. Popelensky","doi":"10.1134/S1061920825600096","DOIUrl":"10.1134/S1061920825600096","url":null,"abstract":"<p> There is a considerable collection of examples of spaces <span>(X)</span> equipped with an involution <span>(tau)</span> such that the mod 2-cohomology rings <span>(H^{2*}(X))</span> and <span>(H^*(X^tau))</span> are isomorphic. In [4], it was shown that such an isomorphism is a part of a certain structure on the equivariant cohomology of <span>(X)</span> and <span>(X^tau)</span>, which is called an <span>(H)</span><i>-frame</i>. An important part of the <span>(H)</span>-frame structure in [4] was the so-called <i> conjugation equation</i>. In [3], the coefficients of the conjugation equation were calculated in terms of the Steenrod squares. Later, another proofs were obtained, [9, 10]. In this paper, we develop a similar notion of a <span>(Q)</span>-framing, which occurs in the situation when a space <span>(X)</span> is equipped with two commuting involutions <span>(tau_1,tau_2)</span> and the mod 2-cohomology rings <span>(H^{4*}(X))</span> and <span>(H^*(X^{tau_1,tau_2}))</span> are isomorphic. Basic examples are the quaternionic Grassmannians and the quaternionic flag manifolds equipped with two complex involutions. Our main result is the establishment of the quaternionic conjugation equations and identifying their coefficients in terms of Steenrod operations. </p><p> <b> DOI</b> 10.1134/S1061920825600096 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"105 - 122"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spatial Decay/Asymptotics in the Navier–Stokes Equation Navier-Stokes方程的空间衰减/渐近性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920824601812
P. Topalov
{"title":"Spatial Decay/Asymptotics in the Navier–Stokes Equation","authors":"P. Topalov","doi":"10.1134/S1061920824601812","DOIUrl":"10.1134/S1061920824601812","url":null,"abstract":"<p> We discuss the occurrence of spatial asymptotic expansions of solutions to the Navier–Stokes equation on <span>( {mathbb{R}} ^d)</span>. In particular, we prove that the Navier–Stokes equation is locally well-posed in a class of weighted Sobolev and asymptotic spaces. The solutions depend analytically on the initial data and time and (generically) develop nontrivial asymptotic terms as <span>(|x|toinfty)</span>. In addition, the solutions have a spatial smoothing property that depends on the order of the asymptotic expansion. </p><p> <b> DOI</b> 10.1134/S1061920824601812 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"196 - 209"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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