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Mutual singularities of overlapping attractor and repeller
Chaos. 2021. Vol. 31. No. 8. Article 083127 .
We apply the concepts of relative dimensions and mutual singularities to characterize the fractal properties of overlapping attractor and repeller in chaotic dynamical systems. We consider one analytically solvable example (a generalized baker’s map); two other examples, the Anosov–Möbius and the Chirikov–Möbius maps, which possess fractal attractor and repeller on a two-dimensional torus, are explored numerically. We demonstrate that although for these maps the stable and unstable directions are not orthogonal to each other, the relative Rényi and Kullback–Leibler dimensions as well as the mutual singularity spectra for the attractor and repeller can be well approximated under orthogonality assumption of two fractals.
Publication based on the results of:
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 P. 1–16
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
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2026 Vol. 12 No. 1 P. 60–110
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Dedaev R., Zhukova N., Imaev R., Математика и теоретические компьютерные науки 2025 Т. 3 № 3 С. 43–57
Пусть G – группа гомеоморфизмов n-мерного топологического многообразия M с непустым краем ∂M. Целью работы является изучение влияния непустого края многообразия M на структуру глобальных аттракторов группы гомеоморфизмов G. Наш основной результат состоит в доказательстве того, что любой глобальный аттрактор A группы гомеоморфизмов G на многообразии M с непустым краем ∂M либо принадлежит краю и ...
Added: October 17, 2025
Bagaev A., Ганеева Д. М., Журнал Средневолжского математического общества 2025 Т. 27 № 3 С. 287–301
In this paper we consider classical iterated function systems (IFS) consisting of
a finite number of contracting mappings for a complete metric space. The main goal is to
study the class of IFSs whose attractors are Cantor sets, i.e. perfect totally disconnected sets.
Important representatives of this class are totally disconnected IFSs introduced by Barnsley.
We have proposed other ...
Added: September 29, 2025
Bagaev A., Известия высших учебных заведений. Математика 2025 № 10 С. 30–43
In this paper we investigate the attractors of iterated function systems (IFS) consisting of two plane opposite similitudes. The attractor of such IFS is either a connected or completely disconnected set. Sufficient conditions are found under which the attractor of such a IFS is a connected set. For an arbitrary IFS, sufficient conditions are obtained under which its attractor ...
Added: August 28, 2025
Dedaev R., Zhukova N., Russian Journal of Nonlinear Dynamics 2025 Vol. 21 No. 1 P. 85–102
In this work, by a dynamical system we mean a pair (S, X), where S is either a pseudogroup
of local diffeomorphisms, or a transformation group, or a smooth foliation of the manifold X.
The groups of transformations can be both discrete and nondiscrete. We define the concepts of
attractor and global attractor of the dynamical system (S, ...
Added: March 5, 2025
Bagaev A., Журнал Средневолжского математического общества 2023 Т. 25 № 1 С. 519–530
This paper is devoted to a class of self-affine sets on the plane determined by six homotheties. Centers of these homotheties are located at the vertices of a regular hexagon P, and the homothetic coefficients belong to the interval (0, 1). One must note that equality of homothetic coefficients is not assumed. A self-affine set on the plane ...
Added: January 21, 2025
Zhuzhoma E. V., Медведев В. С., Современная математика. Фундаментальные направления 2024 Т. 70 № 3 С. 389–402
One proves the existence of axiom A diffeomorphisms with expanding attractors of any dimensions. ...
Added: November 30, 2024
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 ...
Added: March 31, 2024