This book addresses the global study of finite and infinite
singularities of planar polynomial differential systems, with special
emphasis on quadratic systems. While results covering the degenerate
cases of singularities of quadratic systems have been published
elsewhere, the proofs for the remaining harder cases were lengthier.
This book covers all cases, with half of the content focusing on the
last non-degenerate ones.
The book contains the complete bifurcation diagram, in the 12-parameter
space, of global geometrical configurations of singularities of
quadratic systems. The authors' results provide - for the first time -
global information on all singularities of quadratic systems in
invariant form and their bifurcations. In addition, a link to a very
helpful software package is included. With the help of this software,
the study of the algebraic bifurcations becomes much more efficient and
less time-consuming.
Given its scope, the book will appeal to specialists on polynomial
differential systems, pure and applied mathematicians who need to study
bifurcation diagrams of families of such systems, Ph.D. students, and
postdoctoral fellows.