Seminar Bifurcations in Hamiltonian Systems

Content

Schedule. Wednesday 17:15-19:00.

Dynamical systems describe the evolution of the possible states of the system (forming the phase space) as time varies. In practical examples these systems depend on parameters: for some coefficients the values are only approximately known and other parameters enter from the outset as values to be controlled and adjusted. Bifurcation theory studies how the behaviour of dynamical systems changes under variation of parameters, especially where a quantitatively small change of a parameter value leads to a qualitative change in the dynamics. In Hamiltonian systems some phase space variables can act as parameters.

Contents. Bifurcations of equilibria and periodic orbits. Simplifying co-ordinates, normal form theory. Bifurcation diagrams of systems depending on one or two parameters. Families of conditionally periodic tori, quasi-periodic bifurcations.

Learning goals. After completion of the course, the student

1. is able to rework a given text into a coherent and understandable presentation;
2. has a good understanding of the mathematics in the field of the seminar;
3. can formulate relevant and challenging exercises.

The grade of the course is determined by one or more presentations (together 80%) and the homework assignments accompanying the other presentations (20%).

Evaluation matrix.