Hamiltonian Systems - Summer Semester 2021 - Lecture and Seminar (2+2)

Hamiltonian Systems


This course is part of the diploma programs Mathematik and Wirtschaftsmathematik as well as of the International Master Program Mathematical Physics as a possible course for the module Selected Topics in Analysis. Hence the course language is English.

Along with this course, there is the Seminar "Hamiltonian Systems". This seminar extends the course and is also part of the module 10-MAT-MPSTAN. This seminar will be organized together with the seminar Dynamical Systems which is part of the corresponding course on Dynamical Systems.

The participation in the lecture does not require participation in the seminar.


Lecture and Seminar are organized via a
Moodle course.



Schedule and Begin


  • The lectures are online and live.
  • They are carried out on BigBlueButton, Access and Recordings via the Moodle course.
  • Schedule: Fridays, 13:15-14:45 (changed from Thursdays)
  • Begin: Thursday April 15, 2021


Target Group

  • Students in the Diploma Programs of Mathematik and Wirtschaftsmathematik in 6th or later semester, and
  • students renrolled in the International Program MSc Mathematical Physics, 2nd semester of 1st or 2nd year.


Contents

This course covers selected features from the theory of Hamiltonian Dynamical Systems. Among those are

  • Birkhoff Normal Form for elliptic fixed points
  • Introduction to and aspects of KAM theory
  • Example of the Restricted 3-body Problem
  • if time permits: brief introduction to Floer theory



Requirements

  • The course builds up on general knowledge about dynamical systems.
  • Introductory knowledge of symplectic geometry and Hamiltonian vector fields is helpful but not obligatory.
  • Sufficient skills in analysis (e.g. semesters 1-3 in diploma programs, or modules 12-PHY-MPMP1 and 12-PHY-MPMP2)


Literature

  • A. Katok a. B. Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge Univ. Press, 1995
  • E. Zehnder, Lectures on Dynamical Systems, EMS Textbooks in Mathematics, European Mathematical Society, 2010
  • more to be added


Last modified: Tue Apr 13 2021
Prof. M. Schwarz