Displaying similar documents to “On lopsided systems.”

Five limit cycles for a simple cubic system.

Noel G. Lloyd, Jane M. Pearson (1997)

Publicacions Matemàtiques

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We resolve the centre-focus problem for a specific class of cubic systems and determine the number of limit cycles which can bifurcate from a fine focus. We also describe the methods which we have developed to investigate these questions in general. These involve extensive use of Computer Algebra; we have chosen to use REDUCE.

The null divergence factor.

Javier Chavarriga, Héctor Giacomini, Jaume Giné (1997)

Publicacions Matemàtiques

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Let (P,Q) be a C vector field defined in a open subset U ⊂ R. We call a null divergence factor a C solution V (x, y) of the equation P ∂V/∂x + Q ∂V/ ∂y = ( ∂P/∂x + ∂Q/∂y ) V. In previous works it has been shown that this function plays a fundamental role in the problem of the center and in the determination of the limit cycles. In this paper we show how to construct systems with a given null divergence factor. The method presented in this paper is a generalization of the classical Darboux...