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|Title: ||Abelian integrals and limit cycles|
|Authors: ||DUMORTIER, Freddy|
|Issue Date: ||2006|
|Citation: ||JOURNAL OF DIFFERENTIAL EQUATIONS, 227(1). p. 116-165|
|Abstract: ||The paper deals with generic perturbations from a Hamiltonian planar vector field and more precisely with the number and bifurcation pattern of the limit cycles. In this paper we show that near a 2-saddle cycle, the number of limit cycles produced in unfoldings with one unbroken connection, can exceed the number of zeros of the related Abelian integral, even if the latter represents a stable elementary catastrophe. We however also show that in general, finite codimension of the Abelian integral leads to a finite upper bound on the local cyclicity. In the treatment, we introduce the notion of simple asymptotic scale deformation.|
|ISI #: ||000238729700006|
|Type: ||Journal Contribution|
|Validation: ||ecoom, 2007|
|Appears in Collections: ||Research publications|
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