Results 1 to 10 of about 22,379 (263)
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 inverse integrating factors for polynomial vector fields
Discrete and Continuous Dynamical Systems, 2007 We present some results and one open question on the existence of polynomial inverse integrating factors for polynomial vector fields.
Adam Mahdi +2 more
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A class of polynomial planar vector fields with polynomial first integral
Journal of Mathematical Analysis and Applications, 2015 We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm computes a minimal first integral.
CARLOS Galindo +2 more
exaly +7 more sources
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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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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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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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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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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