Results 1 to 10 of about 359,696 (180)
Stable piecewise polynomial vector fields [PDF]
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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Bounded Polynomial Vector Fields [PDF]
Transactions of the American Mathematical Society, 1990 We prove that, for generic bounded polynomial vector fields in R n {{\mathbf {R}}^n} with isolated critical points, the sum of the indices at all their critical points is ( − 1 ) n {( - 1 ...
Cima, Anna, Llibre, Jaume
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Polynomial reconstruction of staggered unstructured vector fields [PDF]
Theoretical and Applied Mechanics, 2009 Polynomial reconstruction of staggered unstructured vector fields has been considered. Coefficients of such polynomials are determined by the least squares method. Reduction in the rank of the least squares systems caused by the over-specification of the
Vidović Dragan
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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 C. Murza
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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 Poincar 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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Classification of f-biharmonic submanifolds in Lorentz space forms
Open Mathematics, 2021 In this paper, f-biharmonic submanifolds with parallel normalized mean curvature vector field in Lorentz space forms are discussed. When ff is a constant, we prove that such submanifolds have parallel mean curvature vector field with the minimal ...
Du Li
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Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
Mathematics, 2021 This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field
Erik M. Bollt, Shane D. Ross
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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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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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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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