HOME PAGE FOR GRS MA 775: DIFFERENTIAL EQUATIONS

For general information on my office and office hours, please see my home page.

Texts and Related Sources: The topics we cover will be drawn from the following:

• J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.
• D. Arrowsmith, C. Place, An Introduction to Dynamical Systems.
• C. Robinson, Dynamical Systems.
• V. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations.
• V. Arnold, Mathematical Methods of Classical Mechanics.
• K. Meyer, G. Hall, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem.
• K. Meyer, Periodic Solutions of the N-Body Problem.

The depth of coverage will depend on the background and interests of the class (and me). Topics will include:

• Changing Variables: (including changes which preserve special structure as in Hamiltonian systems)
• Local Linearization: Stable/Unstable Manifolds (I like doing the analytic versions of these theorems--we may also look at topological versions)
• Continuation theorems for differential equations: (Good examples are in Ken Meyer's books)
• Local Bifurcation Theory/Normal forms: (Arrowsmith and Place)
• Melnikov Method: (Guckenheimer and Holmes)

That is a long list...we'll have to see what we get through.

Course Requirements:

• Exercises will be assigned periodically.
• You will be expected to give a talk during the last two weeks of the semester on a (differential equations) topic of your choice.