Results 251 to 260 of about 361,038 (279)

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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Polynomial Vector Fields with Prescribed Algebraic Limit Cycles

Geometriae Dedicata, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function

Systems and Control Letters, 2018
Amir Ali Ahmadi, Bachir El Khadir
exaly  

Classification of complex polynomial vector fields in one complex variable

Journal of Difference Equations and Applications, 2010
Kealey Dias
exaly  

Analytical expressions for the gravitational vector field of a 3-D rectangular prism with density varying as an arbitrary-order polynomial function

Geophysical Journal International, 2017
Jianzhong Zhang
exaly