Results 11 to 20 of about 23,327 (265)
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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Poincaré Compactification for Non-polynomial Vector Fields [PDF]
Qualitative Theory of Dynamical Systems, 2020 In this work a theorical framework to apply the Poincaré compactification technique to locally Lipschitz continuous vector fields is developed. It is proved that these vectors fields are compactifiable in the n-dimensional sphere, though the compactified vector field can be identically null in the equator.
José Luis Bravo +2 more
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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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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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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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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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Non-existence criteria for Laurent polynomial first integrals
Electronic Journal of Qualitative Theory of Differential Equations, 2003 In this paper we derived some simple criteria for non-existence and partial non-existence Laurent polynomial first integrals for a general nonlinear systems of ordinary differential equations $\dot x = f(x)$, $x \in \mathbb{R}^n$ with $f(0) = 0$. We show
Shaoyun Shi, Yuzhu Han
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