Results 11 to 20 of about 253,152 (270)
Polynomial inverse integrating factors for polynomial vector fields
Discrete & Continuous Dynamical Systems - A, 2007 We present some results and one open question on the existence of polynomial inverse integrating factors for polynomial vector fields.
Antoni Ferragut +2 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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Complete polynomial vector fields on the complex plane
Topology, 2004 Let \(v=P(z,w)\partial/\partial z + Q(z,w)\partial/\partial w\) be a complete polynomial vector field on the complex plane \(\mathbb C^ 2\). The author proves that then \(v\) is, up to a polynomial change of coordinates, of one of the three types specified in the main theorem of his paper.
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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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Dual active-set algorithm for optimal 3-monotone regression [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2022 The paper considers a shape-constrained optimization problem of constructing monotone regression which has gained much attention over the recent years. This paper presents the results of constructing the nonlinear regression with $3$-monotone constraints.
Gudkov, Alexandr A. +2 more
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Demonstratio Mathematica, 2023 The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R2{{\mathbb{R}}}^{2}, particularly for quadratic systems.
Benterki Rebiha, Belfar Ahlam
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Centralizers of elements in Lie algebras of vector fields with polynomial coefficients
Pracì Mìžnarodnogo Geometričnogo Centru, 2022 \abstract{ukrainian}{ Нехай $\mathbb K$ -- алгебраїчно замкнене поле харатеристики нуль, $A = \mathbb K[x_1,\dots,x_n]$ -- кільце многочленів і $R = \mathbb K(x_1,\dots,x_n)$ -- поле раціональних функцій від $n$ змінних.
Анатолій Петрович Петравчук
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Covariants, Invariant Subsets, and First Integrals [PDF]
Épijournal de Géométrie Algébrique, 2020 Let $k$ be an algebraically closed field of characteristic 0, and let $V$ be a finite-dimensional vector space. Let $End(V)$ be the semigroup of all polynomial endomorphisms of $V$.
Frank Grosshans, Hanspeter Kraft
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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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Equivariant decomposition of polynomial vector fields [PDF]
Communications in Contemporary Mathematics, 2020 To compute the unique formal normal form of families of vector fields with nilpotent linear part, we choose a basis of the Lie algebra consisting of orbits under the action of the nilpotent linear part. This creates a new problem: to find explicit formulas for the structure constants in this new basis. These are well known in the 2D case, and recently
Mokhtari, Fahimeh, Sanders, J.A.
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