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Integrability and beyond

02INB
Physics and Energy

Over deze cursus

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.

Leerresultaten

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.

Voorkennis

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.

Bronnen

  • 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.

Activiteiten

Lectures

Aanvullende informatie

  • Studiepunten
    ECTS 2
  • Contact uren per week
    2
  • Instructeurs
    doc. Marchesiello Antonella Ph.D., doc. Ing. Šnobl Libor Ph.D.
  • Instructievorm
    Hybrid
Als er nog iets onduidelijk is, kijk even naar de FAQ van CTU (Czech Republic).

Aanbod

  • Startdatum

    17 februari 2025

    • Einddatum
      21 september 2025
    • Periode *
      Summer 2024/2025
    • Voertaal
      Engels
    Inschrijvingsperiode gesloten
Dit aanbod is voor studenten van TU/e (The Netherlands)