Matematicheskii Sbornik
Peer-review mathematical journal
Editor-in-chief
- Boris S. Kashin, Member of the Russian Academy of Sciences, Doctor of physico-mathematical sciences, Professor
Founders
- Russian Academy of Sciences
- Steklov Mathematical Institute of RAS
Main webpage: https://www.mathnet.ru/eng/sm
About
Frequency
The journal is published monthly.
Indexation
- Russian Science Citation Index (elibrary.ru)
- Math-Net.Ru
- MathSciNet
- zbMATH
- Google Scholar
- Ulrich's Periodical Directory
- WorldCat
- CrossRef
- Scopus
- Web of Science
Scope
The journal publishes original scientific research containing full results in the author's field of study in the field of mathematical analysis, ordinary differential equations, partial differential equations, mathematical physics, geometry and topology, algebra and number theory, and functional analysis.
Main webpage: https://www.mathnet.ru/sm
English version, Sbornik: Mathematics 1064-5616 (print), 1468-4802 (online)
Access to the English version journal dating from the first translation volume is available at https://www.mathnet.ru/eng/sm.
Current Issue
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Vol 215, No 11 (2024)
$n$-valued groups, branched coverings and hyperbolic 3-manifolds
Abstract
The theory of $n$-valued groups and its applications is developed by going over from groups defined axiomatically to combinatorial groups defined by generators and relations. A wide class of cyclic $n$-valued groups is introduced on the basis of cyclically presented groups. The best-known cyclically presented groups are the Fibonacci groups introduced by Conway. The problem of the existence of the orbit space of $n$-valued groups is related to the problem of the integrability of $n$-valued dynamics. Conditions for the existence of such spaces are presented. Actions of cyclic $n$-valued groups on $\mathbb R^3$ with orbit space homeomorphic to $S^3$ are constructed. The projections $\mathbb R^3 \to S^3$ onto the orbit space are shown to be connected, by means of commutative diagrams, with coverings of the sphere $S^3$ by three-dimensional compact hyperbolic manifolds which are cyclically branched along a hyperbolic knot. Bibliography: 54 titles.
Matematicheskii Sbornik. 2024;215(11):3-32
3-32
33-64
Classification of nonsingular four-dimensional flows with a untwisted saddle orbit
Abstract
The topological equivalence of low-dimensional Morse–Smale flows without fixed point (NMS-flows) under assumptions of various generality is the subject of a number of publications. Starting from dimension 4, there are only few results on classification. However, it is known that there exists nonsingular flows with wildly embedded invariant saddle manifolds. In this paper the class of nonsingular Morse–Smale flows on closed orientable 4-manifolds with a unique saddle orbit which is, moreover, nontwisted, is considered. It is shown that the equivalence class of a certain knot embedded in $\mathbb S^2\times\mathbb S^1$ is a complete invariant of such a flow. Given a knot in $\mathbb S^2\times\mathbb S^1$, a standard representative in the class of flows under consideration is constructed. The supporting manifold of all such flows is shown to be the manifold $\mathbb S^3\times\mathbb S^1$.Bibliography: 24 titles.
Matematicheskii Sbornik. 2024;215(11):65-91
65-91
Saddle connections
Abstract
It is shown that vector fields that are close to a fixed field with the same set of connections form a smooth Banach submanifold. A sufficient condition for the birth of saddle connections in a generic family is presented. The following result is proved: in a perturbation of a monodromic hyperbolic polycycle of $n$ connections in a generic family at least $n$ limit cycles can appear.Bibliography: 21 titles.
Matematicheskii Sbornik. 2024;215(11):92-121
92-121
Lower semicontinuity of relative entropy disturbance and its consequences
Abstract
It is proved that the decrease of quantum relative entropy under the action of a quantum operation is a lower semicontinuous function of the pair of its arguments. This property implies, in particular, that the local discontinuity jumps of the quantum relative entropy do not increase under the action of quantum operations. It also implies the lower semicontinuity of the modulus of the joint convexity of quantum relative entropy (as a function of ensembles of quantum states).Various corollaries and applications of these results are considered.Bibliography: 42 titles.
Matematicheskii Sbornik. 2024;215(11):122-156
122-156