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Mathematical Physics 3: Integrable Systems of Classical Mechanics   (WS 2012)


Schedule

Lectures   Dr. Matteo Petrera Tue  12:15 - 13:45  MA 742
  Dr. Matteo Petrera Thu  12:15 - 13:45  MA 742

This is a course of the Berlin Mathematical School held in English.


Office hours

Name Office hours Room
Lectures   Dr. Matteo Petrera          Wed 10:00 - 12:00   MA 819


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Contents

  • Structures on manifolds and Lie algebras (vector fields, distributions, differential forms, Lie groups, Lie algebras).

  • Hamiltonian systems on Poisson manifolds (Hamiltonian mechanics, bi-Hamiltonian manifolds, local and global structures, Lie-Poisson structures, construction of Poisson manifolds).

  • Finite-dimensional integrable systems on Poisson manifolds (Liouville integrability, action-angle variables, Adler-Kostant-Symes theorems, R-brackets, Lax operators, r-matrix hierarchies).

  • Examples of finite-dimensional integrable systems (Olshanetsky-Perelomov projection method, Calogero-Moser systems, Toda lattice, Gaudin model).


Literature

  • M. Petrera, Lecture Notes (complete version, 25.03.2013, 176 pages. In the next future, some small changes/corrections are possible. Please refer to the latest version when you start preparing your exam!).
  • Yu.B. Suris, The Problem of Integrable Discretization: Hamiltonian Approach, Birkhaeuser Verlag, 2003.
  • O. Babelon, D. Bernard, M. Talon, Introduction to Classical Integrable Systems, Cambridge University Press, 2003.

Schein

  • There is no Tutorial.
  • To get the Schein for the oral exam, you need to attend at least 75% of the course.

Matteo Petrera . 29.01.2013