In the last three decades, advances in methods for investigating
polynomial ideals and their varieties have provided new possibilities
for approaching two long-standing problems in the theory of differential
equations: the Poincaré center problem and the cyclicity problem
(the problem of bifurcation of limit cycles from singular trajectories).
Using a computational algebra approach, the book addresses the
center and cyclicity problems as behaviors of dynamical systems
and families of polynomial systems.
In the talk we discuss briefly the main topics of the book:
properties of ideals in polynomial rings and their affine varieties normal forms of differential equations the problem of distinguishing between a center and a focus the isochronicity problem invariants of differential equations the cyclicity problem
Seminarsko predavanje bo v ponedeljek 15. junija 2009 ob 15:15 uri v seminarski sobi CAMTP, Krekova 2, pritličje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.