The course aims to develop the basic concepts and methods of Hamiltonian description for the study of complex and chaotic dynamics of systems with applications in physics and technology.
Content:
Formalism and methods of Hamilton mechanics:
Canonical variables and symplectic formalism.
Canonical transformations and generating functions.
Poisson bracket formalism.
Infinitesimal canonical transformations, symmetries, and invariant quantities.
Hamilton-Jacobi theory, integrability, and separability.
Action-angle variables and adiabatic invariants.
Near-integrable systems and Canonical Perturbation Theory.
Complex dynamics and chaos:
Resonances and the problem of small denominators.
Poincaré maps and surfaces of section.
Kolmogorov-Arnold-Moser theorem and Hamiltonian chaos.
Criteria for transition to chaos.
Stochastic approximation and diffusion in phase space.
Applications:
Forced, parametrically excited, and coupled nonlinear oscillators.
Non-linear interaction of charged particles with electromagnetic fields.
- Teacher: Ιωάννης Κομίνης
ECTS : 4
Language : el