Results 31 to 40 of about 12,423 (291)
A new approach to integrals of discretizations by polarization [PDF]
Open Communications in Nonlinear Mathematical PhysicsRecently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields.
Yuri B. Suris
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Bifurcation at Infinity in Polynomial Vector Fields
Journal of Differential Equations, 1993 We study here the appearance of limit cycles from the equator in polynomial vector fields with no singular points at infinity: this bifurcation is a generalized Hopf bifurcation from the point at infinity. We start with the general theory and then specialize to the particular case of cubic polynomial systems for which we study the simultaneous ...
Blows, T.R., Rousseau, C.
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Polynomial representations of classical Lie algebras and flag varieties
Physics Letters B, 2022 Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields.
A. Morozov +3 more
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Topological enumeration of complex polynomial vector fields [PDF]
Ergodic Theory and Dynamical Systems, 2014 AbstractThe enumeration of combinatorial classes of the complex polynomial vector fields in$ \mathbb{C} $presented by K. Dias [Enumerating combinatorial classes of the complex polynomial vector fields in$ \mathbb{C} $.Ergod. Th. & Dynam. Sys. 33(2013), 416–440] is extended here to a closed form enumeration of combinatorial classes for degree$d ...
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Limit cycles of planar polynomial vector fields
Scholarpedia, 2010 Maoan Han, Jibin Li, Chengzhi Li
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Generic polynomial vector fields are not integrable
Indagationes Mathematicae, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maciejewski, Andrzej J +2 more
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Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors
Complexity, 2021 Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method.
Mingshu Chen +3 more
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On a certain functional equation in the algebra of polynomials with complex coefficients
Abstract and Applied Analysis, 2006 Many analytical problems can be reduced to determining the number of roots of a polynomial in a given disc. In turn, the latter problem admits further reduction to the generalized Rauss-Hurwitz problem of determining the number of roots of a polynomial ...
E. Muhamadiev
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Journal of Mechatronics, Electrical Power, and Vehicular Technology, 2023 The stability analysis of a DC-DC buck converter is a challenging problem due to the hybrid systems characteristic of its dynamics. Such a challenge arises from the buck converter operation which depends upon the ON/OFF logical transitions of its ...
Tua A. Tamba, Jonathan Chandra, Bin Hu
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Stable Planar Polynomial Vector Fields
Revista Matemática Iberoamericana, 1985 Let \(\chi_ n\) be the vector space of polynomial vector fields in \(R^ 2\) with coefficients of degree \(\leq n\). Every \(X\in \chi_ n\) transported to the upper hemisphere \(S^ 2_+\) by the central projection and normalized suitably extends to an analytic vector field \({\mathcal P}(X)\) on \(S^ 2\).
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