Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668811 | Bulletin des Sciences Mathématiques | 2014 | 15 Pages |
Abstract
The period annuli of the planar vector field xâ²=âyF(x,y), yâ²=xF(x,y), where the set {F(x,y)=0} consists of k different isolated points, is defined by k+1 concentric annuli. In this paper we perturb it with polynomials of degree n and we study how many limit cycles bifurcate, up to a first order analysis, from all the period annuli simultaneously in terms of k and n. Additionally, we prove that the associated Abelian integral is piecewise rational and, when k=1, the provided upper bound is reached. Finally, the case k=2 is also treated.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
S. Pérez-González, J. Torregrosa,