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The topological classification of diffeomorphisms of the two-dimensional torus with an orientable attractor
Russian Journal of Nonlinear Dynamics. 2020. Vol. 16. No. 4. P. 595–606.
This paper is devoted to the topological classification of structurally stable diffeomorphisms of the two-dimensional torus whose non-wandering set consists of an orientable one-dimensional attractor and finitely many of isolated source and saddle periodic points, under the assumption that the closure of the union of the stable manifolds of isolated periodic points consists of simple pairwise non-intersecting arcs. The classification of one-dimensional basis sets on surfaces is exhaustively obtained in papers by V. Grines. He also obtained a classification of some classes of structurally stable diffeomorphisms of surfaces using combined algebra-geometric invariants. In this paper, we distinguish a class of diffeomorphisms that admit purely algebraic differentiating invariants.
Publication based on the results of:
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
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Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
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Bolbachan V., / Series math "arxiv.org". 2024.
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Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
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Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
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Added: May 14, 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 ...
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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, ...
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Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
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Medvedev V., / Series arXiv "math". 2026.
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Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
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Kolesnikov A., / Series arXiv "math". 2025.
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Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
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Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
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Popov V., / Series arXiv "math". 2025. No. 2502.01539.
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Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
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Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
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Dedaev R., Zhukova N., Imaev R., Математика и теоретические компьютерные науки 2025 Т. 3 № 3 С. 43–57
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Bagaev A., Ганеева Д. М., Журнал Средневолжского математического общества 2025 Т. 27 № 3 С. 287–301
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Bagaev A., Известия высших учебных заведений. Математика 2025 № 10 С. 30–43
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Dedaev R., Zhukova N., Russian Journal of Nonlinear Dynamics 2025 Vol. 21 No. 1 P. 85–102
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Nozdrinova E., Pochinka O., Tsaplina E., Moscow Mathematical Journal 2024 Vol. 24 No. 1 P. 21–39
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other trajectories of the system. If there is a way to choose this pair so that the space orbits in ...
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