Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Although this systematic study of autonomous systems begins with a thorough treatment of linear systems, the main emphasis is on local and global behavior of nonlinear systems. The main purpose of this revised edition is to introduce students to the qualitative and geometric theory of ordinary differential equations as well as serving as a reference book for mathematicians researching dynamical systems. Readers 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 to rival that which we have of linear flows.