Differential Equations and Dynamical Systems
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This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behavior of nonlinear systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations originated by at the end of the 19th century. It is also intended as a reference book for mathematicians doing research on dynamical systems. There are several new features in this book such as the simplified pr...
This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behavior of nonlinear systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations originated by at the end of the 19th century. It is also intended as a reference book for mathematicians doing research on dynamical systems. There are several new features in this book such as the simplified proof of the Hartman-Grobman Theorem and examples illustrating the proof, map in the theory of limit cycles, an efficient method for obtaining the global phase portrait of two-dimensional systems, and the description of the behavior of a one-parameter family of limit cycles. Readers of this book will find that, except for certain topics of current mathematical research such as the number of limit cycles and the nature of attracting sets of dynamical systems, the global qualitative theory of a nonlinear dynamical system leads to an understanding of the solution set of the nonlinear system that rivals the understanding what we have of linear flows.