Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 807: Dynamical Systems (Spring)

Sergey Bolotin (Spring 2018)

Description: The main theme of the course will be Hamiltonian dynamical systems. This classical subject goes back to Poincare. Hamiltonian systems play a growing role in mathematics, including symplectic topology and partial differential equations. The course will start with a survey of the Hamiltonian formalism and basic symplectic geometry. Then we discuss completely integrable systems, perturbation theory of Hamiltonian systems,  elements of KAM theory and Aubry--Mather theory. The last  topic will be chaotic behavior in Hamiltonian systems.

Grading will be based on homework.

Prerequisites: Real analysis (Math 522) and ordinary differential equations (Math 319 or 320). Some knowledge of differential geometry (Math 761) will be helpful.

Textbook: For the first part of the course we'll use: V.I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, 60. Springer-Verlag, New York.
For later subjects we'll use mostly lecture notes.

credits: 
3 (N-A)
semester: 
InFrequent
prereqs: 
Math 522 and some ODE course

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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