Results 31 to 40 of about 253,152 (270)
On the polynomial vector fields on [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2011 Let X be a polynomial vector field of degree n on M, M = ℝm. The dynamics and the algebraic-geometric properties of the vector fields X have been studied intensively, mainly for the case when M = ℝm, and especially when n = 2. Several papers have been dedicated to the study of the homogeneous polynomial vector field of degree n on $\mathbb{S}^2 ...
Jaume Llibre, Yulin Zhao
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Transversal conics and the existence of limit cycles [PDF]
, 2014 This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincar\'e--Bendixson regions by using transversal conics.
Giacomini, Héctor, Grau, Maite
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A new approach to integrals of discretizations by polarization [PDF]
Open Communications in Nonlinear Mathematical PhysicsRecently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields.
Yuri B. Suris
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Polynomial representations of classical Lie algebras and flag varieties
Physics Letters B, 2022 Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields.
A. Morozov +3 more
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Topological enumeration of complex polynomial vector fields [PDF]
Ergodic Theory and Dynamical Systems, 2014 AbstractThe enumeration of combinatorial classes of the complex polynomial vector fields in$ \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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Spiralling dynamics near heteroclinic networks [PDF]
, 2013 There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a {two parameter family of vector fields} on the three-dimensional sphere $\EU^3$, whose flow has a ...
Address Of Alex +7 more
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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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Self-Duality beyond Chiral p-Form Actions [PDF]
, 2000 The self-duality of chiral p-forms was originally investigated by Pasti, Sorokin and Tonin in a manifestly Lorentz covariant action with non-polynomial auxiliary fields. The investigation was then extended to other chiral p-form actions. In this paper we
Coleman +11 more
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Realization problems for limit cycles of planar polynomial vector fields [PDF]
, 2015 We show that for any finite configuration of closed curves $\Gamma\subset \mathbb{R}^2$, one can construct an explicit planar polynomial vector field that realizes $\Gamma$, up to homeomorphism, as the set of its limit cycles with prescribed periods ...
Margalef-Bentabol, Juan +1 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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