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Planar Dynamical Systems - Selected Classical Problems (Hardcover, Digital original)
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Planar Dynamical Systems - Selected Classical Problems (Hardcover, Digital original)
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In 2008, November 23-28, the workshop of "Classical Problems on
Planar Polynomial Vector Fields " was held in the Banff
International Research Station, Canada. Called "classical
problems", it was concerned with the following: (1) Problems on
integrability of planar polynomial vector fields. (2) The problem
of the center stated by Poincare for real polynomial differential
systems, which asks us to recognize when a planar vector field
defined by polynomials of degree at most n possesses a singularity
which is a center. (3) Global geometry of specific classes of
planar polynomial vector fields. (4) Hilbert's 16th problem. These
problems had been posed more than 110 years ago. Therefore, they
are called "classical problems" in the studies of the theory of
dynamical systems. The qualitative theory and stability theory of
differential equations, created by Poincare and Lyapunov at the end
of the 19th century, had major developments as two branches of the
theory of dynamical systems during the 20th century. As a part of
the basic theory of nonlinear science, it is one of the very active
areas in the new millennium. This book presents in an elementary
way the recent significant developments in the qualitative theory
of planar dynamical systems. The subjects are covered as follows:
the studies of center and isochronous center problems, multiple
Hopf bifurcations and local and global bifurcations of the
equivariant planar vector fields which concern with Hilbert's 16th
problem. The book is intended for graduate students, post-doctors
and researchers in dynamical systems. For all engineers who are
interested in the theory of dynamical systems, it is also a
reasonable reference. It requires a minimum background of a
one-year course on nonlinear differential equations.
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