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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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Polynomial Vector Fields on Algebraic Surfaces of Revolution
Results in Mathematics, 2020The 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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Polynomial vector fields on the torus
Bulletin of the Brazilian Mathematical Society, 1986In 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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On the isoclines of polynomial vector fields
Siberian Mathematical Journal, 1994The 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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On Muldowney’s Criteria for Polynomial Vector Fields with Constraints
2011We study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields. Using the formulation of Muldowney's sufficient criteria for excluding periodic orbits of the parameterized vector field on a convex set as a quantifier elimination problem over the ordered field of ...
Hassan Errami +3 more
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On a Polynomial Vector Field Model for Shape Representation
2006In this paper we propose an efficient algorithm to perform a polynomial approximation of the vector field derived from the usual distance mapping method. The main ingredients consist of minimizing a quadratic functional and transforming this problem in an appropriate setting for implementation.
Mickael Chekroun +2 more
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An analogue rotated vector field of polynomial system
Applied Mathematics and Mechanics, 2000zbMATH 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, 1990A 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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A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function
IEEE Conference on Decision and Control and European Control Conference, 2011We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.
Amir Ali Ahmadi +2 more
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Complete polynomial vector fields in a ball
2004Summary: We describe the complete polynomial vector fields in the unit ball of a Euclidean space.
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