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Attractors. Then and now
Russian Mathematical Surveys. 2023. Vol. 78. No. 4. P. 635–777.
S. V. Zelik
This survey is based on a number of mini-courses taught by the author at the University of Surrey (UK) and Lanzhou University (China). It discusses the classical and modern results of the theory of attractors for dissipative PDEs, including attractors for autonomous and non-autonomous equations, dynamical systems in general topological spaces, various types of trajectory, pullback and random attractors, exponential attractors, determining functionals and inertial manifolds, as well as the dimension theory for the classes of attractors mentioned above. The theoretical results are illustrated by a number of clarifying examples and counterexamples
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular
L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings
between the links and a bounded length of the maximum link that does not depend on the network
size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in
the ...
Added: July 8, 2026
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Kuksin S., Zhang H., Stochastic Processes and their Applications 2020 No. 130 P. 4721–4745
We prove that well posed quasilinear equations of parabolic type, perturbed by bounded nondegenerate random forces, are exponentially mixing for a large class of random forces. ...
Added: April 2, 2025
Grines V., Pochinka O., Chilina E., / Series math "arxiv.org". 2023.
The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate to a class of homeomorphisms for which the restriction of the map to a connected component of the non-wandering set ...
Added: December 20, 2023
Sheshmani A., Long C., Vafa C. et al., Communications in Mathematical Physics 2023 Vol. 399 No. 3 P. 1991–2043
We study extremal non-BPS black holes and strings arising in M-theory
compactifications on Calabi–Yau threefolds, obtained by wrapping M2 branes on nonholomorphic
2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor
mechanism we compute the black hole mass and black string tension, leading to a conjectural
formula for the asymptotic volumes of connected, locally volume-minimizing
representatives of non-holomorphic, even-dimensional ...
Added: August 29, 2023
Zelik S., Ильин А. А., Костянко А. Г., Математические заметки 2022 Т. 111 № 1 С. 54–66
We prove the existence of a global attractor of a regularized Euler–Bardina system with dissipation on the two-dimensional sphere and in arbitrary domains on the sphere. Explicit estimates for the fractal dimension of the attractor in terms of its physical parameters are obtained. ...
Added: May 9, 2023
Seržant I., Moroz G., Humanities and Social Sciences Communications 2022 Vol. 9 Article 58
Efficiency is central to understanding the communicative and cognitive underpinnings of language. However, efficiency management is a complex mechanism in which different efficiency effects—such as articulatory, processing and planning ease, mental accessibility, and informativity, online and offline efficiency effects—conspire to yield the coding of linguistic signs. While we do not yet exactly understand the interactional ...
Added: January 23, 2022
Springer Nature Switzerland AG, 2019.
Gathering the proceedings of the 11th CHAOS2018 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the ...
Added: October 29, 2021
Stanislav Minkov, Shilin I., Qualitative Theory of Dynamical Systems 2021 Vol. 20 No. 3 Article 77
For Milnor, statistical, and minimal attractors, we construct examples of smooth flows ϕ on S^2 for which the attractor of the Cartesian square of ϕ is smaller than the Cartesian square of the attractor of ϕ. In the example for the minimal attractors, the flow ϕ also has a global physical measure such that its ...
Added: September 16, 2021
Stanislav Minkov, Ivan Shilin, / Series math "arxiv.org". 2020. No. arXiv:2011.04824.
For Milnor, statistical, and minimal attractors, we construct examples of smooth flows φ on S^2 for which the attractor of the Cartesian square of φ is smaller than the Cartesian square of the attractor of φ. In the example for the minimal attractors, the flow φ also has an SRB-measure such that its square does ...
Added: November 12, 2020
Bekmaganbetov K., Chechkin G., Chepyzhov V. V. et al., Discrete and Continuous Dynamical Systems 2017 Vol. 37 No. 5 P. 2375–2393
We consider the 3D Navier--Stokes systems with randomly rapidly oscillating right--hand sides. Under the assumption that the random functions are ergodic and statistically homogeneous in space variables or in time variables we prove that the trajectory attractors of these systems tend to the trajectory attractors of homogenized 3D Navier--Stokes systems whose right--hand sides are the ...
Added: June 7, 2017
Minkov S. S., Okunev A., Functional Analysis and Its Applications 2016 Vol. 50 No. 1 P. 48–53
We prove that, for any E u ⊕ E cs partially hyperbolic C 2 diffeomorphism, the ω-limit set of a generic (with respect to the Lebesgue measure) point is a union of unstable leaves. As a corollary, we prove a conjecture made by Ilyashenko in his 2011 paper that the Milnor attractor is a union of unstable leaves. In the paper mentioned above, Ilyashenko reduced the ...
Added: May 4, 2016
Volk D., Discrete and Continuous Dynamical Systems 2014 Vol. 34 No. 5 P. 2307–2314
Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In this paper, we prove the finiteness conjecture for the ITMs of three intervals. Namely, the subset of ITMs of finite ...
Added: December 30, 2015
Volk D., Kleptsyn V., Moscow Mathematical Journal 2014 Vol. 14 No. 2 P. 339–365
A one-dimensional confined nonlinear random walk is a tuple of N diffeomorphisms of the unit interval driven by a probabilistic Markov chain. For generic such walks, we obtain a geometric characterization of their ergodic stationary measures and prove that all of them have negative Lyapunov exponents. These measures appear to be probabilistic manifestations of physical measures for ...
Added: December 30, 2015
Volk D., Ergodic Theory and Dynamical Systems 2014 Vol. 34 No. 2 P. 693–704
For a smooth manifold of any dimension greater than one, we present an open set of smooth endomorphisms such that any of them has a transitive attractor with a non-empty interior. These maps are m-fold non-branched coverings,m≥3. The construction applies to any manifold of the form S 1×M, where S 1 is the standard circle and Mis an arbitrary manifold. ...
Added: December 28, 2015
Ilyashenko Y., Shilin I., Proceedings of the Steklov Institute of Mathematics 2012 Vol. 277 No. 1 P. 84–93
There are different non-equivalent definitions of attractors in the theory of dynamical systems. The most common are two definitions: the maximal attractor and the Milnor attractor. The maximal attractor is by definition Lyapunov stable, but it is often in some ways excessive. The definition of Milnor attractor is more realistic from the physical point of ...
Added: February 5, 2013