Math 557A, Dynamical Systems, Fall 2011

General information: COURSE: Math 557A, Fall 2011.
LECTURE MEETING TIME: TH 12:30-1:45pm
LECTURE MEETING LOCATION: Math 501
TEXTBOOK: Nonlinear oscillators, dynamical systems and bifurcations of vector fields by J. Guckenheimer and P. Holmes

Instructor: NAME: Qiudong(Don) Wang
OFFICE: Math 313
PHONE: 621-8307
EMAIL: dwang@math.arizona.edu
WEB-ADDRESS: http://www.math.arizona.edu/~dwang
Office Hours: TH 9:00-10:30

This is a graduate level introductory course to the modern theory of dynamical systems. The following is a list of detailed contents.

Introductory Remarks [Lecture Notes]

Unit 1: 1D Dynamics: Periodic Orbits, Sarkovskii Theorem [Lecture Notes] [Alternating Proof]
Symbolic Coding, Kneading Theory [Lecture Notes]
Circle Diffeomorphisms, Denjoy Theory [Lecture Notes]

Unit 2: Hyperbolic Dynamics: Anosov Diffeomorphism [Lecture Notes]
Local Hyperbolic Structure, Stable and Unstable Manifold [Lecture Notes]
Smale's Horseshoe, Homoclinic Tangle [Lecture Notes]
Milnikov's Method [Lecture Notes]

Unit 3: Elliptic Dynamics: Conformal Mappings Around Fixed Points [Lecture Notes]
Area Preserving Maps and Normal Forms [Lecture Notes]
The KAM Theory [Lecture Notes]

If there are enough interest at the end of the semester, then this class will continue to run for another semester (Math 557B), in which we will cover Ergoidc Theory and Bifurcation Theory.

Home work will be assigned, and should be turned in in a timely manner. Regular homework assignment will be counted for 60% of your grade. You can collaborate in solving the problems but the written up you turn in should be your own. There will also be a final exam, which will be counted for 20% of your final grade. The remaining 20% is for your class attendence.