CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
Phone +(386) (2) 2355 350 and 2355 351 $\bullet$ Fax +(386) (2) 2355 360
Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoretično fiziko

Presentation of the new book by
V. G. Romanovski and D.S. Shafer
"The Center and Cyclicity Problems: A Computational Algebra Approach", Boston-Basel-Berlin: Birkhäuser, 2009

Professor Dr. Valery G. Romanovski
CAMTP, University of Maribor

Abstract: 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:
$\bullet$ properties of ideals in polynomial rings and their affine varieties $\bullet$ normal forms of differential equations $\bullet$ the problem of distinguishing between a center and a focus $\bullet$ the isochronicity problem $\bullet$ invariants of differential equations $\bullet$ 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.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --