Deze cursusinformatie geeft aan hoe het onderwijs zal verlopen bij pandemieniveau code geel en groen.
Als er tijdens het academiejaar aangepast wordt naar code oranje of rood, zijn er wijzigingen mogelijk o.a. in de gebruikte werk - en evaluatievormen.

Integrable Hamiltonian systems

Course Code :2600WETIHS
Study domain:Mathematics
Academic year:2020-2021
Semester:1st semester
Contact hours:60
Credits:6
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:English
Exam period:exam in the 1st semester
Lecturer(s)Sonja Hohloch

3. Course contents *

  1. Definition of Hamiltonian systems, basic properties & examples.
  2. Integrability in finite dimensions (Frobenius, Liouville, more general notions), basic properties, examples.
  3. Important examples of integrable systems in mathematics and physics: Spherical pendulum, rigid body, top (Lagrange, Euler, Kovalevskaya), coupled spin oscillators, coupled angular momenta...
  4. Local behaviour (regular points): Theorem of Arnold-Liouville, transformation to action-angle coordinates.
  5. Local behaviour (singular points): local normal form of Eliasson-Miranda-Zung for nondegenerate singular points in terms of hyperbolic, elliptic, and focus-focus components.
  6. Toric systems: Symplectic classification by Delzant by means of polygons.
  7. Semitoric systems: properties and interaction with the topology and geometry of the underlying manifold.
  8. Integrability in infinite dimensions ("integrable Hamiltonian partial differential equations"): motivation and important examples (Korteweg-de Vries, Sine-Gordon, Nonlinear Schrödinger equation).