MATH 8540 - Advanced Topics in Ordinary Differential Equations and Dynamic Systems

3 Credit Hours
Prerequisites: Math 4275 or MATH 6275 with grade of C or higher.
Description
(Same as Phys 8540.) This course is a graduate-level presentation of the mathematical theory of ordinary differential equations and nonlinear dynamical systems. It is designed for students who want to study the advanced topics of qualitative theory of ordinary differential equations and do research in dynamical systems Topics include existence and uniqueness theorems; IVP and Picard iterates; stability; variational equation and Floquet theory; Jordan normal form; the center manifold theorem; relaxation oscillations and method of averaging; Smale horseshoe and transverse homoclinic orbits; Lyapunov exponents and topological entropy.