r Presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. The text provides a systematic introduction to such methods as division of an analytic family of functions in its ideal of coefficients and asymptotic expansion of non-differentiable return maps and desingularisation. The exposision moves from classical analytic geometric methods to regular limit periodic sets to more recent tools for singular limit sets.
Robert Roussarie was Professor of Mathematics at the University of Burgundy, France.
Preface.- 1 Families of Two-dimensional Vector Fields.- 2 Limit Periodic Sets.- 3 The 0-Parameter Case.- 4 Bifurcations of Regular Limit Periodic Sets.- 5 Bifurcations of Elementary Graphics.- 6 Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets.- Bibliography.- Index.
"A well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in recently developed methods. The book, reflecting the state of the art, can also be used for teaching special courses." --Mathematical Reviews