Complex Hamiltonian Dynamics and Applications
|Flow||F - Physics|
|Category||Obligatory by selection|
|Class Hours - Lab Hours||3 - 0|
|Lecturers||Ioannis Kominis (School of AMPS)|
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.