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Топологическая сопряженность n-кратных декартовых произведений грубых преобразований окружности
Известия высших учебных заведений. Прикладная нелинейная динамика. 2021. Т. 29. № 6. С. 851–862.
Golikova L., Зинина С. Х.
It is known from the 1939 work of A. G. Mayer that rough transformations of the circle are limited to the
diffeomorphisms of Morse – Smale. A topological conjugacy class of orientation-preserving diffeomorphism is entirely determined by its rotation number and the number of its periodic orbits, while for orientation-changing diffeomorphism the topological invariant will be only the number of periodic orbits. Thus, the purpose of this study is to find topological invariants of 𝑛-fold Cartesian products of diffeomorphisms of a circle. Methods. This paper explores the rough Morse – Smale diffeomorphisms on the 𝑛-torus surface. To prove the main result, additional constructions and formation of subsets of considered sets were used. Results. In this paper, a numerical topological invariant is introduced for 𝑛-fold Cartesian products of rough circle transformations. Conclusion.The criterion of topological conjugacy of 𝑛-fold Cartesian products of rough transformations of a circle is formulated.
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., Sivkin V., Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
Белоусов Н. М., Черепанов Л. К., Деркачов С. Э. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Муравьев М. Ю., Annales mathématiques du Québec (Канада) 2025
Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Interpreting his approach in terms of differential forms permits to generalize these results to a much broader context. The spectrum of the absolute boundary problem for ...
Added: May 6, 2026
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 2026
Монахова Э. А., Монахов О. Г., Rzaev E. et al., Прикладная дискретная математика 2026 Т. 71 С. 112–127
В настоящей работе исследовано совместное конструирование топологий семейств оптимальных по диаметру циркулянтных сетей $C(N; \pm 1, \pm s_2)$ и реализуемых для них оптимальных алгоритмов маршрутизации сложности $O(1)$. Предлагаемый алгоритм маршрутизации основан на использовании масштабируемых параметров $L$-образных шаблонов плотной укладки графов на плоскости для семейств оптимальных сетей.
Определены аналитические формулы зависимости этих параметров от диаметра графов семейств ...
Added: May 4, 2026
Dudakov S., Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 12 P. 6092–6102
We study the additive theory of arbitrary figures in linear spaces, that is, the theory of
addition extended to sets of vectors. Our main result is the following: if a linear space is infinite,
then the additive theory of figures admits interpreting second-order arithmetic and, therefore, it has
such or higher degree of undecidability. For countably infinite spaces, ...
Added: May 1, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Domrin V. I., Malova H. V., V. Yu. Popov et al., Cosmic Research 2026 Vol. 64 No. 2 P. 238–252
During magnetospheric perturbations a relatively thin current sheet with thickness about several
proton gyroradii forms in the Earth’s magnetotail. In a framework of the kinetic model describing current
sheet thinning in the magnetotail, the processes of its formation are investigated depending on the normal
magnetic field magnitude which affects both the current sheet structure and particle dynamics within ...
Added: April 27, 2026
Tsareva O. O., Malova H. V., V. Yu. Popov et al., Plasma Physics Reports 2026 Vol. 52 No. 2 P. 179–185
The influence of asymmetry of plasma sources on the structure and spatial localization of a superthin
current sheet (STCS) supported by demagnetized electrons is studied using a self-consistent model. The
simulation takes into account the presence of a single plasma source in the northern hemisphere, which
makes the plasma flow asymmetric. It is demonstrated that the asymmetry of ...
Added: April 27, 2026
Pochinka O., Yakovlev E., Shmukler V., Russian Journal of Nonlinear Dynamics 2026
Every discrete dynamical system (cascade) generated by a homeomorphism induces a continuous
dynamic system (flow) — a suspension. However, not every flow is equivalent to a suspension
over a cascade, a necessary and sufficient condition for this is the existence of a global
section for the flow. In the case of the existence, the flow is equivalent to ...
Added: April 24, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 25
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP ...
Added: April 23, 2026
Kazaryan M., Lando S., Kodaneva N., Journal of Geometry and Physics 2026 No. 225 Article 105841
Weight systems associated to the Lie algebras 𝔤𝔩(N) for N = 1,2,... can be unified into auniversal one. The construction is based on an extension of the 𝔤𝔩(N) weight systems to permutations. This universal weight system takes values in the algebra of polynomials C[N;C1,C2,...] in infinitely many variables. We show that under the substitution Cm ...
Added: April 23, 2026
Kychkin A., Chernitsin I., Прикладная информатика 2026 Т. 21 № 1 С. 40–58
The results of the development of a software microservice embedded in atmospheric air quality monitoring systems to support the identification of industrial pollution sources are presented. The emission and subsequent spread of harmful substances in the lower layers of the atmosphere is dynamic and characterized by high uncertainty due to the specific features of technological ...
Added: April 23, 2026
Козырева В. С., Богомазов А. И., Демков Б. П. et al., Астрономический журнал 2023 Т. 100 № 5 С. 441–451
В работе изучается световое уравнение затменной двойной системы FL Lyr по данным космических телескопов Kepler и TESS. Показано, что в системе есть кандидат в экзоюпитеры FL Lyr b с вероятным значением орбитального периода около 22 лет. ...
Added: March 5, 2026
Gafurova D., Sergey Aksenov, Regular and Chaotic Dynamics 2025 Vol. 30 No. 6 P. 969–991
The circular restricted three-body problem is used as an approximate model in space mission planning. Its periodic solutions around equilibrium points, which are referred to as the libration points, are utilized for exploration of possible spacecraft trajectories in the preliminary stages of mission design. In this paper, a numerical methodology for periodic libration point orbits ...
Added: November 24, 2025
Gurevich E., Saraev I., Communications in Nonlinear Science and Numerical Simulation 2026 Vol. 152 No. D Article 109301
We consider homeomorphisms with a finite and topologically hyperbolic chain-recurrent set and explore the interrelation between the structure of the chain-recurrent set and the topology of carrying manifolds of dimension n > 3. We demonstrate that the Lefschetz fixed-point theorem can be refined for this class of homeomorphisms as follows: if the (n-1)-dimensional invariant manifold ...
Added: October 4, 2025
Glutsyuk A., Александров А. А., Горский А. С., / Series arXiv "math". 2025.
In this study, we discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrodinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the ...
Added: June 23, 2025
Barinova M., Osenkov E., Pochinka O., Regular and Chaotic Dynamics 2025 Vol. 30 No. 2 P. 226–253
In investigating dynamical systems with chaotic attractors, many aspects of global behavior of a flow or a diffeomorphism with such an attractor are studied by replacing a nontrivial attractor by a trivial one [1, 2, 11, 14]. Such a method allows one to reduce the original system to a regular system, for instance, of a Morse – Smale ...
Added: April 8, 2025
Eugene Osenkov, Pochinka O., Moscow Mathematical Journal 2025 Vol. 25 No. 1 P. 79–90
One of the fundamental results of three-dimensional topology is the Kneser–Milnor unique decomposition theorem. If a 3-manifold admits a Morse–Smale diffeomorphism without heteroclinic curves, the topology of the decomposition summands can be substantially refined. For orientable 3-manifolds this was done by C. Bonatti, V.Z. Grines, V.S. Medvedev and E. Pecou in 2002. In the present ...
Added: March 31, 2025
E.Y. Gurevich, I.A. Saraev, Partial Differential Equations in Applied Mathematics 2024 Vol. 11 Article 100759
We study relations between a structure of non-wandering set of a Morse–Smale diffeomorphism f and its carrying closed manifold M^n. We prove that if f has no any saddle periodic points with one-dimensional unstable manifolds, and for any periodic point p of Morse index (n−1) its unstable manifolds do not intersect stable invariant manifolds of saddle periodic points different from ...
Added: June 22, 2024