MATH 642 (Fall 2014)

       Dynamical systems I

 

       Instructor: Vadim Kaloshin

MATH 3111, vadim.kaloshin@gmail.com, (301) 405-5132.

 

Course Information

closely related class Math670

 

 

The course will be devoted to basic topics in dynamical systems.

 

1.     Foundations of topological dynamics, homeomorphisms, flows, periodic and recurrent points, transitivity and minimality, symbolic dynamics.

2.     Elements of ergodic theory, invariant measures and sets, ergodicity, ergodic theorems, mixing, spectral theory.

3.     Elements of Newtonian and Hamiltonian dynamics, action-angle variables, KAM theory, Newtonian three body problem.

4.     Connection between Hamiltonian and Lagrangian dynamics, Poincare-Cartan invariants.

5.     Elements of symplectic geometry.

 

M. Brin, G. Stuck Introduction to dynamical systems, Cambridge University Press

A. Arnold Mathematical methods of classical mechanics, GTM, Springer, 1989

Lectures: MWF, 11:00--11:50 p.m. Math 1313

Office hours: by appointment.