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.