Planar dynamical systems

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In 2008, a workshop on "Classical Problems on Planar Polynomial Vector Fields" took place at the Banff International Research Station in Canada. This workshop focused on integrability issues of planar polynomial vector fields, the center problem posed by Poincaré regarding when a planar vector field defined by polynomials of degree at most n has a center singularity, and the global geometry of specific classes of these vector fields. Additionally, Hilbert’s 16th problem was discussed. These topics, considered "classical problems," have been relevant in the study of dynamical systems for over 110 years. The qualitative and stability theories of differential equations, developed by Poincaré and Lyapunov in the late 19th century, have evolved significantly as vital branches of dynamical systems throughout the 20th century and remain active in the new millennium. This book presents recent advancements in the qualitative theory of planar dynamical systems in an accessible manner. Topics include center and isochronous center problems, multiple Hopf bifurcations, and local and global bifurcations of equivariant planar vector fields related to Hilbert’s 16th problem. It is aimed at graduate students, post-doctoral researchers, and those in the engineering field with a basic understanding of nonlinear differential equations.