Results 11 to 20 of about 12,485 (261)
Stable piecewise polynomial vector fields
Electronic Journal of Differential Equations, 2012 Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector ...
Claudio Pessoa, Jorge Sotomayor
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Polynomial Vector Fields on the Clifford Torus [PDF]
International Journal of Bifurcation and Chaos, 2021 First, we characterize all the polynomial vector fields in [Formula: see text] which have the Clifford torus as an invariant surface. Then we study the number of invariant meridians and parallels that such polynomial vector fields can have on the Clifford torus as a function of the degree of these vector fields.
Jaume Llibre, Adrian Calin Murza
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Bounded Polynomial Vector Fields [PDF]
Transactions of the American Mathematical Society, 1990 We prove that, for generic bounded polynomial vector fields in R
Cima, Anna, Llibre, Jaume
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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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Isochronicity and commutation of polynomial vector fields [PDF]
Siberian Mathematical Journal, 1999 21 pages, LaTeX, 5 PostScript ...
Volokitin, E. P., Ivanov, V. V.
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Invariants of polynomial vector fields
Journal of Differential Equations, 2023 We characterize the existence of first integrals and invariants (first integrals depending on the time) for the polynomial vector fields which are invariant under an involution.
Llibre, Jaume, Valls, Claudia
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Twin Polynomial Vector Fields of Arbitrary Degree
Bulletin of the Brazilian Mathematical Society, New Series, 2021 In this paper we study polynomial vector fields on C2 of degree larger than 2 with n2 isolated singularities. More precisely, we show that if two polynomial vector fields share n2-1 singularities with the same spectra (trace and determinant) and from these singularities n2-2 have the same positions, then both vector fields have identical position and ...
Llibre, Jaume, Valls, Clàudia
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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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Explicit Geometric Integration of Polynomial Vector Fields [PDF]
BIT Numerical Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mclachlan, Robert Iain. +1 more
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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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