Perko L. Differential Equations and Dynamical Systems
It seems that you're in Germany. We have a dedicated site for Germany. This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems. The text succeeds admiraby
Marsden L. Sirovich M. Golubitsky Advisors G.
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This course provides an introduction to the dynamics of ordinary differential equations. Specific topics include existence theory, linear and nonlinear systems of ordinary differential equations, stability theory of equilibrium solutions, invariant manifolds, elementary bifurcation theory, strange attractors. It will also be demonstrated how these methods can be used in applications. Our first meeting is on Tuesday, Sept. If you have time, please try to familiarize yourself with the material by reading the introduction and prepare for the fruitful work this semester. Hope it will be an enjoyable one! You are allowed to bring one formula sheet.