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Integrability and beyond

02INB
Physics and Energy

About this course

Abstract: Hamiltonian systems and their integrals of motion. Hamilton-Jacobi equation and separation of variables. Classification of integrable systems with integrals polynomial in momenta. Superintegrability. Perturbative methods in the study of Hamiltonian systems.

Learning outcomes

The students will get a deeper knowledge of the classical Hamiltonian mechanics, better understand the motivation for various standard notions and be able to follow more recent advances in the field, like perturbative methods and superintegrability.

Course requirements

Essential: classical analytical mechanics (canonical momenta, Hamilton’s equations of motion etc.), cf. course 02TEF1 Theoretical Physics 1. Recommended: basic knowledge of differential geometry (manifolds, vector fields, differential forms), cf. course 02GMF1 Geometric Methods of Physics 1.

Resources

  • Key references:
  • [1] W. Thirring, Classical Mathematical Physics: Dynamical Systems and Field Theories, Springer 2003.
  • [2] M. Audin: Hamiltonian Systems and Their Integrability. American Mathematical Society, 2008.
  • [3] W. Miller Jr., S. Post and P. Winternitz: Classical and quantum superintegrability with applications, J. Phys. A: Math. Theor. 46 423001, 2013.
  • Recommended references:
  • [4] E. G. Kalnins, J. M. Kress and W. Miller Jr.: Separation of variables and superintegrability : the symmetry of solvable systems, Institute of Physics Publishing, 2018.
  • [5] J. A. Sanders, F. Verhulst, J. Murdock: Averaging Methods in Nonlinear Dynamical Systems, Springer 2007.

Activities

Lectures

Additional information

  • Credits
    ECTS 2
  • Contact hours per week
    2
  • Instructors
    doc. Marchesiello Antonella Ph.D., doc. Ing. Šnobl Libor Ph.D.
  • Mode of instruction
    Hybrid
If anything remains unclear, please check the FAQ of CTU (Czech Republic).

Offering(s)

  • Start date

    17 February 2025

    • Ends
      21 September 2025
    • Term *
      Summer 2024/2025
    • Instruction language
      English
    • Register between
      24 Oct - 24 Nov 2024
    Enrolment open
    Apply now
These offerings are valid for students of TUM (Germany)