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On the Structure of Orbits from a Neighborhood of a Transversal Homoclinic Orbit to a Nonhyperbolic Fixed Point
Regular and Chaotic Dynamics. 2025. Vol. 30. No. 1. P. 9–25.
Gonchenko S., Gordeeva O. V.
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 description of the structure of the set Nμ of all orbits entirely lying in a sufficiently small fixed neighborhood of the homoclinic orbit. Moreover, we show that for μ 0 the set Nμ is hyperbolic (for μ = 0 it is nonuniformly hyperbolic) and the dynamical system fμ N μ (the restriction of fμ to Nμ) is topologically conjugate to a certain nontrivial subsystem of the topological Bernoulli scheme of two symbols
Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6
This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...
Added: May 26, 2026
Ilyashenko Y., Shilin I., Stanislav Minkov, Russian Journal of Mathematical Physics 2026 Vol. 33 No. 1 P. 89–106
In this paper, new numerical invariants of structurally unstable vector fields in the plane
are found. One of the main tools is an improved asymptotics of sparkling saddle connections that
occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological
invariant of two arithmetic progressions, both perturbed and unperturbed, on the ...
Added: May 26, 2026
Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2025 Vol. 299 No. 6
The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...
Added: May 25, 2026
Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856
AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...
Added: May 23, 2026
Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...
Added: May 23, 2026
Kibkalo Vladislav, Chertopolokhov V., Mukhamedov A. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...
Added: May 22, 2026
Морозов С. В., Calcolo 2026 Vol. 63 No. 2 Article 23
The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
Added: May 22, 2026
Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 Article 18
A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
Added: May 21, 2026
Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 No. 106192
The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders ...
Added: May 20, 2026
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Gurevich E., Saraev I., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 19–56
In this paper, we consider a class of gradient-like ows without heteroclinic
intersections, dened on closed manifolds of dimension four. We show that for
such ows, the problem of complete topological classication can be reduced to
the combinatorial problem of distinguishing special framed graphs describing
the mutual arrangement of invariant manifolds and the action of the ow on a
wandering ...
Added: May 18, 2026
Gonchenko S., Lerman L., Turaev D., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Khutorskaya O., Stepochkina A. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Lerman L., Gonchenko S. V., Shilnikov A. L. et al., 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 ...
Added: March 18, 2025
Кулагин Н. Е., Лерман Л.М., Известия высших учебных заведений. Прикладная нелинейная динамика 2024 Т. 32 № 6 С. 878–896
Bounded stationary (i.e. independent in time) spatially one-dimensional solutions of a quasilinear parabolic PDE are studied on the whole real line. Its stationary solutions are described by a nonlinear ODE of the sixth order of the Euler–Lagrange–Poisson type and therefore can be transformed to the Hamiltonian system with three degrees
of freedom being in addition reversible with respect ...
Added: November 21, 2024
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
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
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