Complex Hamiltonian Dynamics and Applications
| Code | 9.3.3398.7 |
|---|---|
| Semester | 9th |
| Flow | F - Physics |
| Category | Obligatory by selection |
| Credits | 4 |
| Class Hours - Lab Hours | 3 - 0 |
| Lecturers | Ioannis Kominis (School of AMPS) |
Description
Formalism and methods of Hamiltonian mechanics: Canonical variables and symplectic formalism. Canonical transformations and generating functions. Poisson brackets formulation. Infinitesimal canonical transformations, symmetries and invariants. Hamilton-Jacobi theory, integrability and separability. Action-angle variables and adiabatic invariants. Near-integrable systemsand Canonical Perturbation theory. Complex dynamics and chaos: Resonances and the problem of small denominators. Poincaré surfaces of section and maps. Kolmogorov-Arnold-Moser theorem and Hamiltonian chaos. Criteria for extended chaoticity. Stochastic approximation and diffusion in phase space. Applications: Forced, parametrically driven and coupled nonlinear oscillators. Nonlinear interactions of charged particles with electromagnetic fields.