Pri založbi Bürkhauser je izšla znanstvena monografija z naslovom The Center and Cyclicity Problems A Computational Algebra Approach, katere avtorja sta Valery G. Romanovski in Douglas S. Shafer.
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: Birkhauser, 2009.
Professor Dr. Valéry 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:
• 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