Last updated June 21, 2001
Hamiltonian structures and evolution equations
  1. Symplectic and Poisson manifolds. The Darboux theorem.
  2. Finite-dimensional Hamiltonian formalism. Integrable Hamiltonian systems.
  3. The Schouten bracket. Deformations and the Hamiltonian cohomology. An algebraic model for the Poisson geometry.
  4. Jet bundles. The spectral sequence of an integrable distribution. The one-line theorem: variational complex.
  5. Infinite-dimensional Hamiltonian systems.
  6. The symmetries and conservation laws of Hamiltonian equations. The integrability of infinite-dimensional systems.
  7. Bi-Hamiltonian equations: the Magri theorem and hierarchies of soliton equations.
  8. Examples and perspectives.
Questions and suggestions should go to J. S. Krasil'shchik, josephk @ diffiety.ac.ru.