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ИНТЕГРИРУЕМЫЕ СИСТЕМЫ НА КАСАТЕЛЬНОМ РАССЛОЕНИИ К МНОГОМЕРНОЙ СФЕРЕ
Вестник Самарского государственного университета. Естественнонаучная серия. 2014. № 7 (118). С. 60–69.
Pokhodnya N., Шамолин М. В.
The systems which have finite-dimensional spheres as the space of positions, are arising in many problems of multi-dimensional dynamics. Accordingly, tan- gent bundles of those spheres become phase spaces of such systems. In the article activity of inductive transition in the system on tangent bundle of low-dimen- sional sphere under increase of its dimension and absence of force field is ana- lyzed. At that, nonconservative fields of forces are presented with the presence of which the systems possess the complete choice of first integrals expressing in terms of finite combination of elementary functions and are, in general, the transcendental functions of its variables.
A. S. Baybar, M. Yu. Puzachenko, R. B. Sandlersky, Geography and Natural Resources 2025 Vol. 46 No. S1 P. S15–S22
This article presents a methodology for landscape mapping based on the integration of long-term series of multispectral data and morphometric characteristics of the relief for various hierarchical levels. Using the example of the Central Forest Reserve and its adjacent territory, where both indigenous and anthropogenically modified geosystems are combined, it is shown that the identification ...
Added: January 14, 2026
Агапов С. В., Уфимский математический журнал 2025 Т. 17 № 4 С. 3–10
Исследуются обыкновенные дифференциальные уравнения второго порядка, которым удовлетворяют следующие специальные функции: функция Бесселя, гипергеометрическая функция, эллиптическая функция Вейерштрасса. Доказано, что все эти уравнения являются метризуемыми, в явном виде построены соответствующие метрики. Доказано, что во всех вышеперечисленных случаях уравнения геодезических допускают линейный по импульсам первый интеграл. ...
Added: November 20, 2025
Pogrebkov A., Теоретическая и математическая физика 2023 Т. 217 № 3 С. 577–584
We consider some generalizations of a (2 + 1)-dimensional Davey–Stewartson-type equation. In particular,
we propose a dynamical system that does not admit an explicit formulation in terms of differential equations, but needs an additional independent variable. ...
Added: January 24, 2025
Gontsov R., Poberezhny V. A., Хельминк Г., Успехи математических наук 2011 Т. 66 № 1 С. 65–110
Added: January 1, 2025
Alexeevskaya E., Вестник арбитражной практики 2018 № 4 С. 3–5
The lack of a uniform understanding of the "judicial system" definition in Russia in the legal literature leads to a budgetary resource dispersion, which, ultimately, negatively affects the quality of justice and, as a result, destabilize the judicial system. Besides, the legal science lacks true comprehension of the Russian judicial system phenomenon, which prevents the ...
Added: August 20, 2024
Blank M., Nonlinearity 2024 Vol. 37 No. 6 Article 065006
We propose a novel unifying approach to study the shadowing property
for a broad class of dynamical systems (in particular, discontinuous and non-invertible)
under a variety of perturbations. In distinction to known constructions, our approach is local:
it is based on the gluing property which takes into account the shadowing under a single
(not necessarily small) perturbation. ...
Added: April 17, 2024
Blank M., Современная математика. Фундаментальные направления 2023 Т. 69 № 1 С. 50–61
A new approach based on the analysis of the influence of a single perturbation is proposed as a test for the shadowing property for a broad class of dynamical systems (in particular, non-autonomous) under a variety of perturbations. Applications for several interesting cases are considered in detail. ...
Added: March 23, 2024
Bialy M., Fierobe C., Glutsyuk A. et al., Arnold Mathematical Journal 2022 Vol. 8 P. 411–422
This is a collection of problems composed by some participants of the workshop “Differential Geometry, Billiards, and Geometric Optics” that took place at CIRM on October 4–8, 2021. ...
Added: February 1, 2024
Michael Blank, Mathematika 2023 Vol. 69 No. 2 P. 349–365
The purpose of this work is threefold:
(i) extend shadowing theory for discontinuous and non-invertible systems,
(ii) consider more general classes of perturbations (for example, small only on average),
(iii) establish a general theory based on the property that the shadowing holds
for the case of a single perturbation. The ``gluing'' construction used in the analysis
of the last property ...
Added: March 21, 2023
Bibilo Y., Glutsyuk A., Nonlinearity 2022 Vol. 35 No. 10 P. 5427–5480
The tunnelling effect predicted by Josephson (Nobel Prize, 1973) concerns the Josephson junction: two superconductors separated by a narrow dielectric. It states existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modelled by a family of differential equations on two-torus depending on three parameters: B (abscissa), A (ordinate), ω ...
Added: December 20, 2022
Белоусов Н. М., Записки научных семинаров ПОМИ РАН 2020 Т. 494 С. 5–22
В заметке приводится новый вывод преобразования Бэклунда для нелинейного уравнения Шредингера. Обсуждается, какие ему соответствуют сохраняющиеся величины и как оно связано с методом обратной задачи. Кроме того, строится квантовый аналог преобразования Бэклунда, задаваемый Q-оператором Бакстера. ...
Added: November 8, 2022
Blank M., [б.и.], 2022.
The purpose of this work is threefold: (i) extend shadowing theory
for discontinuous and non-invertible systems, (ii) consider more
general classes of perturbations (for example, small only on average),
(iii) establish a general theory based on the property that the
shadowing holds for the case of a single perturbation. The “gluing”
construction used in the analysis of the last property ...
Added: June 26, 2022
Pokhodnya N., Шамолин М. В., Вестник Самарского государственного университета. Естественнонаучная серия 2013 № 9-1 (110) С. 35–41
Certain general conditions of integrability in elementary functions for the systems on the tangent bundle of two-dimensional sphere are studied. At that an interesting example of three-dimensional phase pattern of pendulum-like system which describes the motion of spherical pendulum, placed in an over-run medium flow. Sufficient conditions of existence of the first integrals expressed through ...
Added: December 14, 2021
Glutsyuk A., / Series "Working papers by Cornell University". 2021. No. 2104.01362.
Reflection in strictly convex bounded planar billiard acts on the space of oriented lines and preserves a standard area form. A caustic is a curve C whose tangent lines are reflected by the billiard to lines tangent to C. The famous Birkhoff conjecture states that the only strictly convex billiards with a foliation by closed ...
Added: November 4, 2021
Glutsyuk A., Journal of Fixed Point Theory and Applications 2022 Vol. 24 No. 2 Article 35
For a given closed convex planar curve γ with smooth boundary and a given p>0, the string construction yields a family of curves Γp for which γ is a caustic. The action of the reflection Tp on the tangent lines to γ≃S1 induces its action on the tangency points: a circle diffeomorphism Tp:γ→γ. We say ...
Added: November 4, 2021
Kochetkov Y., / Series Arxiv. math "Cornell university preprint series". 2021. No. 2106.15557.
Let us consider a family F(alpha,beta,gamma,delta) of convex quadrangles in the plane with given angles
{alpha,beta,gamma,delta} and with the perimeter 2pi. Such quadrangle Q from F(alpha,beta,gamma,delta) can be
considered as a point (x_1,x_2,x_3,x_4) in 4-dimensional space R^4, where {x_1,x_2,x_3,x_4} --- lengths of edges. Then to F a finite open segment I in R^4 is corresponded. A quadrangle in F, that corresponds to the midpoint of I$is called a balanced quadrangle. ...
Added: June 30, 2021
Kuptsov P., Kuptsova A. V., Stankevich N., Russian Journal of Nonlinear Dynamics 2021 Vol. 17 No. 1 P. 5–21
We suggest a universal map capable of recovering the behavior of a wide range of dynamical systems given by ODEs. The map is built as an artificial neural network whose weights encode a modeled system. We assume that ODEs are known and prepare training datasets using the equations directly without computing numerical time series. Parameter ...
Added: April 3, 2021
Guglielmi N., Protasov V., SIAM Journal on Matrix Analysis and Applications 2018 Vol. 39 No. 4 P. 1642–1669
We consider the problem of computing the closest stable/unstable nonnegative matrix
to a given real matrix. The distance between matrices is measured in the Frobenius norm. The
problem is addressed for two types of stability: the Schur stability (the matrix is stable if its spectral
radius is smaller than one) and the Hurwitz stability (the matrix is stable ...
Added: October 30, 2019
Los A., Ермакова А. Ю., В кн.: Компьютерные науки и информационные технологии: Материалы Международной научной конференции.: Саратов: Издательство Саратовского университета, 2009. С. 144–148.
В статье продолжены исследования методов прогнозирования динамики изменения состояний стохастической системы, первоначально заданных в виде табличной функции (узловые точки). Основной метод построения прогнозной модели – поиск непрерывной «аппроксимирующей» функции, наиболее близко отстоящей от заданных узловых точек. В работе предложенный метод применяется для прогнозирования появления инцидентов, приводящих к нарушению информационной безопасности. Полученные результаты могут применяться для ...
Added: December 11, 2018
Hutsalyuk A., Liashyk A., Pakuliak S. Z. et al., Nuclear Physics B 2018 Vol. 926 P. 256–278
We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(m|n)-invariant R-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the norm obeys a number of properties that uniquely fix it. We also show that a Jacobian of the system ...
Added: September 13, 2018