A semitoric integrable Hamiltonian system, briefly a semitoric system, is given by two autonomous Hamiltonian systems on a 4-dimensional manifold whose flows Poisson- commute and induce an (S1×R)-action that has only nondegenerate, nonhyperbolic sin- gularities. Semitoric systems have been symplectically classified a couple of years ago by Pelayo & Vu Ngoc by means of five invariants. Two of these five invariants are the so-called Taylor series invariant and the twisting index. The first one describes the behaviour near the focus-focus singular fibre and the second one compares the ‘distinguished’ torus action given near each focus-focus singular fiber to the global toric ‘background action’. Recently there has be made some progress in computing these two invariants and, in this talk, we present the (results of the) finished and ongoing project with J. Alonso (Antwerp), H. Dullin (Sydney), and J. Palmer (Rutgers): - Taylor series and twisting index for coupled spin oscillator and coupled angular momenta. - Putting the twisting index in relation with wellknown notions from classical dynamical systems like rotation number, winding number, intersection number etc. - Change of the Taylor series and twisting index when varying the parameters of the systems.
Donnerstag, den 12. Juli 2018 um 10:00-11:00 Uhr, in Mathematikon, INF 205, Konferenzraum, 5. Stock Donnerstag, den 12. Juli 2018 at 10:00-11:00, in Mathematikon, INF 205, Konferenzraum, 5. Stock
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers