Abstract:
Integrable Hamiltonian systems form a special class of Hamiltonian systems which have maximally many Poisson commuting integrals of motion, i.e. half the dimension of the even-dimensional symplectic manifold that forms the phase space of the system. By the Arnold-Liouville-Mineur theorem compact connected components of the regular fibres of the map of integrals have the topology of tori on which one can construct action-angle variables. The motion on these tori is quasi-periodic with the actions being constant in time and the angles increasing with constant rates. Integrable systems play an important role for understanding more general Hamiltonian systems, e.g., from perturbation theory. Moreover, the Bohr-Sommerfeld quantisation of the actions gives a semiclassical approximation of the joint spectrum of quantum systems that have a classical integrable counterpart.
Organizers:
Holger Waalkens
Alexey Bolsinov