On the centers of cubic polynomial differential systems with four invariant straight lines [PDF]
Topological Methods in Nonlinear Analysis, 2020 Assume that a cubic polynomial differential system in the plane has four invariant straight lines in generic position, i.e. they are not parallel and no more than two straight lines intersect in a point. Then such a differential system only can have 0, 1 or 3 centers.
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Dynamics of a physically nonlinear viscoelastic cylindrical shell with a concentrated mass [PDF]
Инженерно-строительный журнал, 2019 It is known that the theory of linear and nonlinear elastic plates and shells is the most developed part of the theory of elasticity. In this area, the necessary equations are obtained and the methods to solve them are developed.
D.A. Khodzhaev +2 more
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Planar Cubic Polynomial Differential Systems with the Maximum Number of Invariant Straight Lines
Rocky Mountain Journal of Mathematics, 2006 We classify all cubic systems possessing the maximum number of invariant straight lines (real or complex) taking into account their multiplicities. We prove that there are exactly 23 topological different classes of such systems. For every class we provide the configuration of its invariant straight lines in the Poincare disc.
Llibre, Jaume, Vulpe, Nicolae
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First Integrals and Phase Portraits of Planar Polynomial Differential Cubic Systems with the Maximum Number of Invariant Straight Lines [PDF]
Qualitative Theory of Dynamical Systems, 2016 In the article LliVul2006 the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial ...
Cristina Bujac +2 more
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Darboux and rational first integrals for a family of cubic three dimensional system
Zanco Journal of Pure and Applied Sciences, 2021 In this paper, we investigate the first integrals of the following system where and , . This kind of system is a special case of three-dimensional polynomial cubic differential systems.
Sarbast H. Mikaeel , Azad I. Amen
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An Algorithm for Higher Order Hopf Normal Forms
Shock and Vibration, 1995 Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit.
A.Y.T. Leung, T. Ge
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Centers of cubic polynomial differential systems
Communications on Pure and Applied AnalysiszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anacona, Gerardo H. +2 more
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The dynamic stability of physically nonlinear plate systems under biaxial compression
Structural Mechanics of Engineering Constructions and Buildings, 2018 The article presents the method of dynamic stability analysis of plate systems with nonshifting ribs. A plate system under the biaxial dynamic compression loads is considered.
Sergey Pavlovich Ivanov +2 more
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Rigid Polynomial Differential Systems with Homogeneous Nonlinearities
MathematicsPlanar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been
Jaume Llibre
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Сomputation of prismatic shells in elastic medium
Инженерно-строительный журнал, 2015 The paper presents a computation procedure of physically nonlinear prismatic shells with the sealed ends. It is known that plates reinforced by stiffening ribs and located in the elastic medium can be calculated in a similar way as uniform ones (without ...
O.G. Ivanov, S.V. Shlychkov
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