Ma 147.
Dynamical Systems (Spring 2007)
Hamiltonian Dynamics
MW 14:30 - 15:55
159 Sloan
Instructor:
Anton Gorodetski
Office: 282 Sloan
Phone: 395-4350
E-mail: asgor@caltech.edu
Office Hours: after the lectures or by appointment
The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. In this course we will develop the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is important object of study. As the main example we will use the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction.
Recommended texts:
1 Arnold V.I., Mathematical methods of classical mechanics
2 Meyer K.R., Hall G.R., Introduction to Hamiltonian dynamics and the N-body problem
Additional references will be given for a few topics not covered by these books.
Grading: Weekly homework 50%, midterm exam 20%, final exam 30%.
Collaboration Policy: You may discuss homework problems with other students, but solutions should be written up individually in your own words. Take-home exams must be your own work.
Famous dynamical systems in motion
Some intriguing open problems in Hamiltonian dynamics
