?
О 3-диффеоморфизмах с обобщенным аттрактором Плыкина
Математический сборник. 2024. Т. 215. № 9. С. 3–29.
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Zhuzhoma E. V., Медведев В. С., Математический сборник 2025 Т. 216 № 11 С. 108–134
В статье для потоков, удовлетворяющих аксиоме А Смейла, на замкнутых многообразиях размерности $n\geq 3$ описывается структура базисных множеств коразмерности один, которые являются либо растягивающимися аттракторами, либо сжимающимися репеллерами. Для таких неперемешивающих базисных множеств строятся специальные захватывающие окрестности с граничными компонентами, гомеоморфными $\mathbb{S}^{n-2}\times\mathbb{S}^1$. Это позволяет построить компактификацию (носитель) бассейна базисного множества, которая является локально тривиальным расслоением ...
Added: November 24, 2025
Kolchurina O., Журнал Средневолжского математического общества 2024 Т. 26 № 3 С. 231–244
В настоящей статье рассматриваются \Omega -устойчивые диффеоморфизмы, заданные на гладких замкнутых ориентируемых многообразиях размерности n \geq 3, все нетривиальные базисные множества которых являются либо растягивающимися аттракторами, либо сжимающимися репеллерами коразмерности 1. Благодаря простой топологической структуре бассейнов аттракторов и репеллеров такого типа можно осуществить переход от данной динамической системы с нетривиальными базисными множествами к регулярной системе, ...
Added: November 9, 2024
Barinova M., Regular and Chaotic Dynamics 2024 Vol. 29 No. 5 P. 794–802
In this paper we consider an Ω-stable 3-diffeomorphism whose chain-recurrent set consists of isolated periodic points and hyperbolic 2-dimensional nontrivial attractors. Nontrivial attractors in this case can only be expanding, orientable or not. The most known example from the class under consideration is the DA-diffeomorphism obtained from the algebraic Anosov diffeomorphism, given on a 3-torus, ...
Added: October 4, 2024
M. K. Barinova, K. Y. Tirskaya, Partial Differential Equations in Applied Mathematics 2024 Vol. 11 Article 100876
The Lyapunov function is a powerful tool for studying dynamical systems. In particular, the existence of such a function for any dynamical system given on compact manifold, established by C. Conley, is the basis for proving the Ω-stability criterion of dynamical systems. Moreover, the Lyapunov function, whose set of critical points of aligns with the chain-recurrent ...
Added: August 22, 2024
Barinova M., / Series math "arxiv.org". 2024.
In the paper we consider an Ω-stable 3-diffeomorphism, chain recurrent set of which consists of isolated periodic points and expanding attractors of codimension 1, orientable or not. We estimate a minimum number of isolated periodic points using information about the structure of the attractors. ...
Added: April 26, 2024
Pochinka O., Таланова Е. А., Математические заметки 2024 Т. 115 № 4 С. 597–609
Настоящая работа посвящена оценке снизу числа критических точек функции Ляпунова для 3-диффеоморфизмов Морса–Смейла с неподвижными точками попарно различных индексов. Известно, что при наличии единственной некомпактной гетероклинической кривой несущим многообразием рассматриваемых диффеоморфизмов является 3-сфера, а класс топологической сопряженности такого диффеоморфизма 𝑓 полностью определяется классом эквивалентности (которых бесконечно много) хопфовского узла 𝐿𝑓 – узла в образующем классе ...
Added: April 15, 2024
Barinova M., Grines V., Pochinka O. et al., Regular and Chaotic Dynamics 2024 Vol. 29 P. 369–375
We consider a topologically mixing hyperbolic attractor Λ⊂M^n for a diffeomorphism f:M^n → M^n of a compact orientable n-manifold M^n, n>3. Such an attractor Λ is called an Anosov torus provided the restriction f|_Λ is conjugate to Anosov algebraic automorphism of k-dimensional torus T^k. We prove that Λ is an Anosov torus for two cases: 1) dimΛ=n−1, dimW^u_x=1, x∈Λ; 2) dimΛ=k,dimW^u_x=k−1,x∈Λ, and Λ belongs to an f-invariant closed k-manifold, 2⩽k⩽n, topologically embedded in M^n. ...
Added: April 15, 2024
Barinova M., Pochinka O., Yakovlev E., Discrete and Continuous Dynamical Systems 2024 Vol. 44 No. 1 P. 1–17
This paper belongs to a series of papers devoted to the study of the structure of the non-wandering set of an A-diffeomorphism. We study such set NW(f) for an Ω-stable diffeomorphism f, given on a closed connected 3-manifold M^3. Namely, we prove that if all basic sets in NW(f) are trivial except attractors, then every non-trivial attractor is ...
Added: November 13, 2023
Barinova M., Grines V., Pochinka O., Труды Математического института им. В.А. Стеклова РАН 2023 Т. 321 С. 45–61
C. Conley’s fundamental theorem of the theory of dynamical systems states that every dynamical system, even a nonsmooth one (i.e., a continuous flow or a discrete dynamical system generated by a homeomorphism), admits a continuous Lyapunov function. A Lyapunov function is strictly decreasing along the trajectories of the dynamical system outside the chain recurrent set ...
Added: September 7, 2023