Results 11 to 20 of about 12,423 (291)

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 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, Jaume Llibre, Adam Mahdi   +2 more
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Generic Complex Polynomial Vector Fields with Real Coefficients [PDF]

Qualitative Theory of Dynamical Systems
The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a complete parametrization of these strata is given in terms of a modulus formed by a combinatorial and an analytic part ...
Jonathan Godin, Christiane Rousseau
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Generic Antiholomorphic Polynomial Vector Fields [PDF]

24 pages, 13 ...
Jonathan A. Godin, Jérémy Perazzelli
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Generic properties of polynomial vector fields at infinity [PDF]

Transactions of the American Mathematical Society, 1969
Enrique A. González Velasco
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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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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, Manuel Fernández, Antonio E. Teruel   +2 more
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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
doaj   +1 more source

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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