Algebraic curves of maximal cyclicity
by
Magdalena Caubergh
Limburgs Universitair Centrum, Universitaire Campus, 3590 Diepenbeek, Belgium

The talk deals with analytic families of planar vector fields, studying methods to detect the cyclicity of a non-isolated closed orbit (the maximum number of limit cycles that can locally bifurcate from it). It is known that this multi-parameter problem can be reduced to a single-parameter one, in the sense that there exist analytic curves in parameter space along which the maximal cyclicity can be attained. In that case one speaks about a maximal cyclicity curve (mcc) in case only the number is considered and of a maximal multiplicity curve (mmc) in case the multiplicity is also taken into account. In view of obtaining efficient algorithms for detecting the cyclicity, we investigate whether such mcc or mmc can be algebraic or even linear depending on certain general properties of the families or of their associated Bautin ideal. In any case by well chosen examples we show that prudence is appropriate.

Date received: May 20, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calh-49.