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## НЕКОТОРЫЕ УСЛОВИЯ ИНТЕГРИРУЕМОСТИ ДИНАМИЧЕСКИХ СИСТЕМ В ТРАНСЦЕНДЕНТНЫХ ФУНКЦИЯХ

Vestnik of Samara University. Natural Science Series. 2013. № 9-1 (110). С. 35-41.

Pokhodnya N., Шамолин М. В.

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 the finite combination of elementary functions, for multi-parametric third order systems are presented.

Pokhodnya N., Шамолин М. В., Вестник Самарского государственного университета. Естественнонаучная серия 2014 № 7 (118) С. 60-69

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 ...

Added: December 14, 2021

Минков С. С., Shilin I., Attractors of direct products / Cornell University. 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

Romaskevich O. L., L'Enseignement Mathématique 2014

We consider 3 -periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have shown that the locus of the centers of inscribed circles of the corresponding triangles is an ellipse. We prove this fact by the complexification of the problem coupled with the complex law of reflection. ...

Added: December 25, 2014

Zabrodin A., Zotov A. V., Lyashik A. et al., Theoretical and Mathematical Physics 2017 Vol. 192 No. 2 P. 1141-1153

We discuss the correspondence between models solved by the Bethe ansatz and classical integrable systems of the Calogero type. We illustrate the correspondence by the simplest example of the inhomogeneous asymmetric six-vertex model parameterized by trigonometric(hyperbolic) functions. ...

Added: October 26, 2017

Chernyat’ev A., Belov A. Y., Communications in Algebra 2010 Vol. 38 No. 7 P. 2588-2605

Let W be an infinite word over finite alphabet A. We get combinatorial criteria of existence of interval exchange transformations that generate the word W. ...

Added: October 1, 2015

Protasov V., Systems and Control Letters 2016 Vol. 90 P. 54-60

We prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slower than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon ...

Added: February 22, 2016

Hutsalyuk A., Lyashik A., Pakuliak S. et al., Russian Mathematical Surveys 2017 Vol. 72 No. 1 P. 33-99

Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians in terms of the current generators of the Yangian double . The method of projections onto intersections of different types of Borel subalgebras of this infinite-dimensional algebra is used to construct the Bethe vectors. Calculation of these projections makes it possible to express the ...

Added: October 26, 2017

Glutsyuk A., Journal of Fixed Point Theory and Applications 2021

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 p:γ→γ. We say ...

Added: November 4, 2021

Blokh A., Oversteegen L., Ptacek R. et al., The parameter space of cubic laminations with a fixed critical leaf / Cornell University. Series math "arxiv.org". 2015.

Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we consider slices of the family of cubic invariant laminations defined by a fixed critical leaf with non-periodic endpoints. We parameterize each slice by ...

Added: February 11, 2015

Springer, 2009

Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics, and ...

Added: February 20, 2013

Belova M., Kudryashov N. A., Regular and Chaotic Dynamics 2016 Vol. 21 No. 3 P. 351-366

Polynomial dynamical systems describing interacting particles in the plane are
studied. A method replacing integration of a polynomial multi-particle dynamical system
by finding polynomial solutions of partial differential equations is introduced. The method
enables one to integrate a wide class of polynomial multi-particle dynamical systems. The
general solutions of certain dynamical systems related to linear second-order partial differential
equations are ...

Added: October 5, 2018

Chernyshev V. L., Толченников А., Наука и образование: электронное научно-техническое издание 2012 Т. 12 № DOI: 10.7463/0113.0515440 С. 143-154

Moving of points on a metric graph associated with the problem of dynamics and statistics of Gaussian packets on a spatial network is under consideration. For an arbitrary tree graph we obtain a representation for the number of points arising from the initial vertex. For a certain graph we find the number of moving points ...

Added: November 13, 2013

Nersisyan A., Zanasi R., International Journal of Robust and Nonlinear Control 1993 Vol. 3 No. 3 P. 199-209

A modified VS feedback is suggested for robust stabilization of continuous-time dynamical systems in the presence of parametric and external time-varying disturbances satisfying the ‘matching conditions’. The main feature of the proposed algorithm is that it contains additional switching ‘integral’ terms which track the unknown disturbances and make it possible to achieve the typical VSS ...

Added: September 10, 2021

Glutsyuk A., Shustin E., Mathematische Annalen 2018 Vol. 372 P. 1481-1501

We show that every polynomially integrable planar outer convex billiard is elliptic. We also
prove an extension of this statement to non-convex billiards. ...

Added: June 29, 2018

Mikheev A. V., Теория. Практика. Инновации 2017 № 9 (21)

In this paper we consider the calculation of a dynamical system described by a second-order differential equation in which a fundamental system of solutions consisting of functions of exponential type is replaced by bounded functions of the Verhulst model. The time dependence of the forces acting on the dynamical system is analyzed, and the obtained ...

Added: September 6, 2017

Filimonov D., Клепцын В. А., Nonlinearity 2014 Vol. 27 No. 6 P. 1205-1223

We study possible one-end finitely presented subgroups of , acting without finite orbits. Our main result, theorem 1, establishes that any such action possesses the so-called property (), that allows one to make distortion-controlled expansion and is thus sufficient to conclude that the action is Lebesgue-ergodic. We also propose a path towards full characterization of ...

Added: October 23, 2014

Afanasiev V., Автоматика и телемеханика 2011 № 4 С. 43-56

The theoretical fundamentals for solving the linear quadratic problems may be some times used to design the optimal control actions for the nonlinear systems. The method relying on the Riccati equation with state-dependent coefficients is promising and rapidly developing tools for design of the nonlinear controllers. The set of possible suboptimal solutions is generated by ...

Added: April 13, 2012

Blokh A., Oversteegen L., Ptacek R. et al., Smart criticality / Cornell University. Series math "arxiv.org". 2014.

A crucial fact established by Thurston in his 1985 preprint is that distinct \emph{minors} of quadratic laminations do not cross inside the unit disk; this led to his construction of a combinatorial model of the Mandelbrot set. Thurston's argument is based upon the fact that \emph{majors} of a quadratic lamination never enter the region between ...

Added: February 11, 2015

Gontsov R., Poberezhny V. A., Helminck G., Russian Mathematical Surveys 2011 Vol. 66 No. 1 P. 63-105

This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical results established for isomonodromic deformations of Fuchsian systems are generalized to the case of integrable ...

Added: September 27, 2013

Afanasiev V., Известия РАН. Теория и системы управления 2011 Т. 9 № 1 С. 24-31

Quite many engineering problems, problems from ecology, medicine, and social sciences are characterized by the presence of factors bringing uncertainty into the corresponding control systems. Additional difficulties for control action construction arise in the case when the objects are described by nonlinear highorder evolutionary equations. An important subset of these objects consists of the object ...

Added: April 13, 2012

Chernyat’ev A., Вестник Московского университета. Серия 1: Математика. Механика 2008 Т. 6 С. 42-44

Added: October 1, 2015

Afanasiev V., Orlov P., Известия РАН. Теория и системы управления 2011 Т. 50 № 3 С. 13-22

An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation (diffeomorphism) transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent ...

Added: April 13, 2012

М.: КомКнига, 2006

В настоящем выпуске публикуются последние достижения в области математического моделирования, управления неоднородными и неопределенными системами, системного анализа, принятия решений, интеллектуальных воспринимающих систем, информатизации общества. Издается на русском и английском языках. ...

Added: April 26, 2015

Volkova L. L., В кн.: Новые информационные технологии в автоматизированных системах: материалы шестнадцатого научно-технического семинара. .: М.: Московский государственный институт электроники и математики, 2013.. С. 317-328.

В статье дан краткий обзор ключевых этапов развития машинной лингвистики в разрезе анализа и синтеза текста. Выделены проблемы работы с языком, являющиеся фундаментальными ограничениями, отделяющими существующий уровень развития отрасли от качественно нового. Рассмотрены перспективные теории, предлагающие новый подход к рассмотрению языка и открывающие возможность заглянуть за барьер машинной лингвистики. ...

Added: January 31, 2018