Planar dynamical systems

Abstract

Preface vii integral on U of system (E). If there exists such an F which is nonconstant on any open subset of U , we say that system (E) is integrable on U .Poincaré and Lyapunov proved the following theorem.Poincaré-Lyapunov Theorem The origin of the polynomial (or analytic) system (E) is a center if and only if in an open neighborhood U of the origin, (E) has a nonconstant first integral which is analytic. Prefacexiii Finally, we would like to acknowledge all members of the Center for Dynamical Systems and Nonlinear Studies of Zhejiang Normal University for their encouragement and help. We thank Mr.Yanchao Zhao of the Science Press of Chinese Academy of Sciences for their help in the publication of this book. We also thank the staff at De Gruyter for their interesting to publish this book and for their useful suggestions to improve the content of this book.