A First Course in the Qualitative Theory of Differential Equations
This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research—including details that other books in the field tend to overlook. Chapters 1—7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8—12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.
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Stability Part I
Linear Equations with Constant Coefficients
Perturbations on Linear Equations
Linear Equations with Periodic Coefficients
Liapunovs Method for Autonomous Equations
Maps and Their Bifurcations
Route to Chaos
The Lorenz System and Strange Attractors
The Smale Horseshoe
PoincaréBendixson Theorem in ÎÎ2
Manifolds and the HartmanGrobman Theorem