Techniques in the Theory of Local Bifurcations: Cyclicity and Desingularization

摘要: A fundamental open question of the bifurcation theory vector fields in dimension 2 is whether number locally bifurcating limit cycles an analytic unfolding bounded, or more precisely, any periodic set has finite cyclicity. In these notes we introduce several techniques for attacking this question: asymptotic expansion return maps, ideal coefficients, desingularization parametrized families. Moreover, because their practical interest, present some partial results obtained by techniques.