?
Scientific Heritage of L. P. Shilnikov. Part II. Homoclinic Chaos
Regular and Chaotic Dynamics. 2025. Vol. 30. No. 2. P. 155–172.
We review the works initiated and developed by L. P. Shilnikov on homoclinic chaos, highlighting his fundamental contributions to Poincar´e homoclinics, periodic orbits, and invariant tori. Additionally, we discuss his related findings in non-autonomous and infinitedimensional systems. This survey continues our earlier review [1], where we examined Shilnikov’s groundbreaking results on bifurcations of homoclinic orbits — his extension of the classical work by A. A. Andronov and E. A. Leontovich from planar to multidimensional autonomous systems — as well as his pioneering discoveries on saddle-focus loops and spiral chaos.
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
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2021 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Shestoperov A. I., Fomina E. V., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., International Frequency Sensor Association (IFSA) Publishing, 19-21 February 2025 Granada, Spain 2025 P. 172–176
The paper presents models for an innovative fully robotic warehouse for storing boxed goods. A discrete multiagent simulation of the movement of shuttles in a warehouse for a given sequence of pallet shipments has been implemented. Different strategies for placement of boxes in various areas of a warehouse are evaluated, as well as optimal routing ...
Added: June 26, 2026
Fedorov Timofey, Moscow Mathematical Journal 2026 Vol. 26 No. 1 P. 73–85
We obtain a complete list of smooth projective threefolds over C for which the dimension of the space of vanishing cycles (in H2(Y,Q) of the smooth hyperplane section Y) equals 2. We also obtain a complete list of rank 2 very ample vector bundles E on smooth projective surfaces with c2(E)=3. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Gonchenko S., Gordeeva O. V., Regular and Chaotic Dynamics 2025 Vol. 30 No. 1 P. 9–25
We consider a one-parameter family fμ of multidimensional diffeomorphisms such that for μ = 0 the diffeomorphism f0 has a transversal homoclinic orbit to a nonhyperbolic fixed point of arbitrary finite order n 1 of degeneracy, and for μ > 0 the fixed point becomes a hyperbolic saddle. In the paper, we give a complete ...
Added: September 18, 2025
Karatetskaia E., Kazakov A., Koryakin V. et al., Regular and Chaotic Dynamics 2024 Vol. 29 No. 5 P. 777–793
We provide a detailed bifurcation analysis in a three-dimensional system describing interaction between tumor cells, healthy tissue cells, and cells of the immune system. As is well known from previous studies, the most interesting dynamical regimes in this model are associated with the spiral chaos arising due to the Shilnikov homoclinic loop to a saddle-focus ...
Added: October 8, 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
Kulagin N., Lev M. Lerman, Konstantin N. Trifonov, Regular and Chaotic Dynamics 2024 Vol. 29 No. 1 P. 40–64
We examine smooth four-dimensional vector fields reversible under some smooth involution L that has a smooth two-dimensional submanifold of fixed points. Our main interest here is about the orbit structure of such system near two types of heteroclinic connections involving saddle-foci and heteroclinic orbits connecting them. In both cases we found families of symmetric periodic orbits, multi-round heteroclinic connections and countable ...
Added: January 18, 2024
V. Z. Grines, L. M. Lerman, Moscow Mathematical Journal 2023 Vol. 23 No. 4 P. 533–544
A class of gradient-like nonautonomous vector fields (NVFs) on a smooth closed manifold M is studied and the following problems are solved: 1) can a gradient-like NVF be constructed by means of the nonautonomous suspension over a diffeomorphism of this manifold, and if so, 1) under what conditions on the diffeomorphism? 2) let a diffeomorphism f be gradient-like (see ...
Added: November 7, 2023
Karatetskaia E., Kazakov A., Stankevich N. et al., Nonlinearity 2023 Vol. 36 No. 7 P. 3501–3541
We study bifurcation mechanisms for the appearance of hyperchaotic attractors in three-dimensional diffeomorphisms, i.e. such attractors whose orbits have two positive Lyapunov exponents in numerical experiments. In particular, periodic orbits belonging to the attractor should have two-dimensional unstable invariant manifolds. We discuss several bifurcation scenarios which create such periodic orbits inside the attractor. This includes cascades ...
Added: October 5, 2023
Gonchenko A. S., Gonchenko S., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 14 P. 3352–3364
We give a short review on discrete homoclinic attractors. Such strange attractors contain only one saddle fixed point and, hence, entirely its unstable invariant manifold. We discuss the most important peculiarities of these attractors such as their geometric and homoclinic structures, phenomenological scenarios of their appearance, pseudohyperbolic properties etc. ...
Added: February 10, 2023
Yu. V. Bakhanova, S. V. Gonchenko, Gonchenko A. S. et al., Journal of difference equations and applications 2023 Vol. 29 No. 9-12 P. 1184–1201
We describe scenarios for the emergence of Shilnikov attractors, i.e. strange attractors containing a saddle-focus with two-dimensional unstable manifold, in the case of threedimensional flows and maps. The presented results are illustrated with various specific examples ...
Added: May 30, 2022
Barinova M., Shustova E., Журнал Средневолжского математического общества 2022 Т. 24 № 1 С. 21–30
A natural way for creating new dynamical systems is to consider direct products of already known systems. The paper studies some dynamical properties of direct products of homeomorphisms and diffeomorphisms. In particular, authors prove that a chain-recurrent set of the direct product of homeomorphisms is a direct product of the chain-recurrent sets. Another result established ...
Added: April 1, 2022
Trifonov K., / Series arXiv "math". 2020. No. 3454820.
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same level of a Hamiltonian and two non-symmetric heteroclinic orbits permuted by the involution. This is a co- dimension one structure and therefore ...
Added: December 26, 2020
Kulagin N., Lerman L., Malkin A., Communications in Nonlinear Science and Numerical Simulation 2021 Vol. 93 Article 105525
Solitons and cavitons (the latter are localized solutions with singularities) for the nonlocal Whitham equations are studied. The fourth order differential equation for traveling waves with a parameter in front of the fourth derivative is reduced to a reversible Hamiltonian system defined on a two-sheeted four-dimensional space. Solutions of the system which stay on one ...
Added: September 16, 2020
Брудный Ю. А., Зайденберг М. Г., Лин В. Я. et al., Успехи математических наук 2019 Т. 74 № 5 С. 170–180
A detailed review of the scientific activities of the remarkable domestic mathematician E. A. Gorin and his results ...
Added: March 17, 2020
Stepanov E., Paolini E., Proceedings of the Royal Society of Edinburgh: Section A 2018 Vol. 148 No. 4 P. 773–818
We show that for a large class of measurable vector fields in the sense of N. Weaver (i.e. derivations over the algebra of Lipschitz functions), the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be ...
Added: December 13, 2018
Kazakov A., Известия высших учебных заведений. Радиофизика 2018 Т. 61 № 8-9 С. 729–738
In this paper, a new scenario of the appearance of mixed dynamics in two-dimensional reversible diffeomorphisms is proposed. The key point of the scenario is a sharp increase of the sizes of both strange attractor and strange repeller which appears due to heteroclinic bifurcations of the invariant manifolds of saddle fixed points belonging to these ...
Added: October 26, 2018