Results 151 to 160 of about 359,696 (180)

Structural Stability of Planar Hamiltonian Polynomial Vector Fields

Proceedings of the London Mathematical Society, 1994
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Jarque, Xavier, Llibre, Jaume
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Polynomial Vector Fields on Algebraic Surfaces of Revolution

Results in Mathematics, 2020
The authors study polynomial vector fields of arbitrary degree in \(\mathbb{R}^3\) having an algebraic surface of revolution invariant by their flows. Subsequently, they restrict their attention to an important case where the algebraic surface of revolution is a cubic surface and characterize all the possible configurations of invariant meridians and ...
Fabio Scalco Dias, Luis Fernando Mello
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Invariant theory of planar polynomial vector fields

2021
The roots of the invariant theory of polynomial vector fields lie in the classical invariant theory. The idea to adapt to polynomial vector fields the concepts of classical invariant theory is due to C. S. Sibirschi, the founder of the Chisinau school of qualitative theory of differential equations.
Joan C. Artés, Jaume Llibre, Dana Schlomiuk, Nicolae Vulpe   +3 more
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Polynomial vector fields on the torus

Boletim da Sociedade Brasileira de Matemática, 1986
In this paper it is shown that the structurally stable polynomial vector fields on the torus \(T^ 2\), with singularities, are open and dense in the set of such vector fields. Many kinds of distinct dynamical phenomena are also presented by a list of examples including the Cherry flows.
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An analogue rotated vector field of polynomial system

Applied Mathematics and Mechanics, 2000
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Polynomial Vector Fields with Prescribed Algebraic Limit Cycles

Geometriae Dedicata, 2001
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Structure and Stability of Gradient Polynomial Vector Fields

Journal of the London Mathematical Society, 1990
A nonlinear Morse-Smale polynomial vector field on the plane need not be structurally stable with respect to perturbation in the set of \(C^ r\) vector fields (Whitney \(C^ r\) topology). By determining the special structure of ``saddles-at-infinity'', it is proved that in the gradient case, the Morse-Smale conditions do imply structural stability in ...
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On the isoclines of polynomial vector fields

Siberian Mathematical Journal, 1994
The author considers autonomous systems (1) \(\dot x = P(x,y)\), \(\dot y = Q(x,y)\) with \(\{P(x,y), Q(x,y)\}\) a polynomial vector field. He proves the following results. Theorem 1. Assume \(P(x,y) = P_m (x,y) + P_n (x,y)\), \(Q(x,y) = Q_m (x,y) + Q_n (x,y)\) with \(m,n > 0\) and \(P_m\), \(Q_m\) and \(P_n\), \(Q_n\) homogeneous polynomials of degree
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Complete polynomial vector fields in a ball

2004
Summary: We describe the complete polynomial vector fields in the unit ball of a Euclidean space.
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Poincaré Compactification of Hamiltonian Polynomial Vector Fields

1995
There exists an extensive literature on changes of variables which transform the equations of motion of interesting problems in Celestial Mechanics into polynomial form (see [Heg]). In most cases this is achieved by regularizing double collisions or introducing redundant variables, or both.
J. Delgado, E. A. Lacomba, J. Llibre, E. Pérez   +3 more
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