Basic Elective

Hamiltonian mechanics

CODE
ΓΘΕ202
SEMESTER
8
HOURS per WEEK
3
ECTS CREDITS
5  (Erasmus+ course)
INSTRUCTOR

Efthymia Meletlidou

Definition of Hamiltonian Mechanics(Hamilton’s equation, symplectic formalism, Poisson’s theorem). Canonical transformations (generating function, symplectic matrices). Infinitesimal canonical transformations (Hamiltonian vector field, infinitesimal symmetries and integrals of motion).  Stability of equilibrium points Liouville’s theorem, Poincare’s theorem. The method of Hamilton-Jacobi, Integrable systems, Lax pairs. Action-angle variables, canonical theory of perturbation, small divisors, K.A.M. theorem. Poincare map, Poincare-Birkhoff theorem, chaotic motion in Hamiltonian systems.

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