Uspekhi Matematicheskikh Nauk
Peer-review bimonthly mathematical journal
Editor-in-chief
- Valery V. Kozlov, Member of the Russian Academy of Sciences, Doctor of physico-mathematical sciences, Professor
Publisher
- Steklov Mathematical Institute of RAS
Founders
- Russian Academy of Sciences
- Steklov Mathematical Institute of RAS
About
Frequency
The journal is published bimonthly.
Indexation
- Scopus
- Web of Science
- Russian Science Citation Index
- Google Scholar
- Ulrich's Periodical Directory
- CrossRef
Scope
The journal publishes survey articles on the most topical research in mathematics, Brief Communications, and biographical materials.
Main webpage: https://www.mathnet.ru/rm
Access to the English version journal dating from the first translation volume is available at https://www.mathnet.ru/eng/umn.
Current Issue
Open Access
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Vol 80, No 5 (2025)
Multidimensional Hamiltonian systems: non-integrability and diffusion
Abstract
Hamiltonian systems of differential equations that are little different from completely integrable systems are under consideration. If such a system is integrable, then the action variables cannot change strongly, and there is no diffusion. Thus the non-integrable behaviour of a Hamiltonian system is closely linked with the diffusion of slow variables. This range of problems is discussed for a subclass of Hamiltonian systems. A new mechanism of diffusion, different from the ‘standard’ scheme of transition chains, is considered on these example. This mechanism is related to the breakdown of a large number of invariant tori of the non-perturbed problem which have almost resonance sets of frequencies. On the formal side, this phenomenon is based on the non-boundedness of integrals of conditionally-periodic functions of time with zero mean.
Uspekhi Matematicheskikh Nauk. 2025;80(5):3-22
3-22
Brief introduction in greedy approximation
Abstract
Sparse approximation is important in many applications because of the concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is based on the concept of sparsity. A fundamental issue of sparse approximation is the problem of the construction of efficient algorithms, which provide good approximation. It turns out that greedy algorithms with respect to dictionaries are very good from this point of view. They are simple in implementation, and there are well-developed theoretical guarantees of their efficiency. This survey/tutorial paper contains a brief description of different kinds of greedy algorithms and results on their convergence and rate of convergence. Also, in Sections 14 and 15 we give some typical proofs of convergence and rate of convergence results for important greedy algorithms and in Section 16 we list some open problems.
Uspekhi Matematicheskikh Nauk. 2025;80(5):23-104
23-104
105-174
Revaz Valer'yanovich Gamkrelidze (obituary)
Uspekhi Matematicheskikh Nauk. 2025;80(5):175-178
175-178
SHORT MESSAGES
Slow convergence of weighted averages for flows and actions of countable amenable groups
Uspekhi Matematicheskikh Nauk. 2025;80(5):179-180
179-180
Change of variables for Sobolev class functions on metric measure spaces
Uspekhi Matematicheskikh Nauk. 2025;80(5):181-182
181-182
A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions
Uspekhi Matematicheskikh Nauk. 2025;80(5):183-184
183-184
On the equivalence of optimal transport problem and action matching with optimal vector fields
Uspekhi Matematicheskikh Nauk. 2025;80(5):185-186
185-186
Impossibility of an embedding of the logic $\operatorname{HC}$ into $\operatorname{IEL}^+$ preserving the classical implication
Uspekhi Matematicheskikh Nauk. 2025;80(5):187-188
187-188
The nonlinear Perron–Frobenius stability problem for cubic stocharic matrices
Uspekhi Matematicheskikh Nauk. 2025;80(5):189-190
189-190