Algebraic and topological classification of the homogeneous cubic vector fields in the plane
Anna Cima,Jaume Llibre +1 more
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This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1990-04-01 and is currently open access. It has received 79 citations till now. The article focuses on the topics: Invariant theory & Complex number.read more
Citations
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Hilbert's 16th problem and bifurcations of planar polynomial vector fields
TL;DR: The progress of study on Hilbert's 16th problem is presented, and the relationship between Hilbert's 15th problem and bifurcations of planar vector fields is discussed.
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Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I)
TL;DR: In this article, a mathematical model of a kind of complicated financial system, and all possible things that the model shows in the operation of our country's macro-financial system are analyzed.
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The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
TL;DR: In this article, the authors studied the centers of planar analytic vector fields which are limit of linear type centers and proved that all the nilpotent centers of these centers are limit-of-linear type centers.
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The focus-centre problem for a type of degenerate system
TL;DR: In this article, a generalized Lyapunov constant was derived for the singular point of a singular vector field in the plane defined by the sum of two homogeneous vector fields, assuming that the origin is a degenerate singular point.
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Limit Cycles Bifurcating from the Period Annulus of Quasi-Homogeneous Centers
TL;DR: In this article, the maximum number of limit cycles bifurcating from the period annulus of any homogeneous and quasi-homogeneous center can be obtained using the Abelian integral method of first order.
References
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Foundations of the theory of algebraic invariants
Book
Invariant theory, old and new
Jean Dieudonné,James B. Carrell +1 more
TL;DR: In this article, the authors present a general linear group representation of the General Linear Group (GL(n, Q) and show that the characters of GL(n; Q) are invariants of antisymmetric tensors.
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Bounded polynomial vector fields
Anna Cima,Jaume Llibre +1 more
TL;DR: In this article, it was shown that for generic bounded polynomial vector fields with isolated critical points, the sum of the indices at all their critical points is (-1) and that there are exactly seventeen different behaviors at infinity for bounded cubic polynomials in the plane.