Conservative Dynamical System

Classical Mechanics deals with dynamical systems without damping or friction. Here think of ideal pendula, springs or tops, the Solar system, etc. We deal with the Newtonian, the Lagrangian (or variational) and the Hamiltonian theory of such systems.

Important issues are the Noether Theorem, that links conservation laws to symmetry and the Liouville Theorem stating the conservation of volume by the phase flow. As a direct consequence of the latter, Hamiltonian systems can't have attractors.

Main part of the theory deals with symplectic manifolds, that also has applications in other parts of physics, like in optics. The language introduced in this course is needed for all reading of modern Dynamical Systems and Mathematical Physics.

Homepages of the course: 
                http://www.math.uu.nl/people/hansmann/cds.html

http://www.math.rug.nl/~cefstat/cds-0809.html