Heinz Hanssmann (Mathematisch Instituut Universiteit Utrecht, Holanda): Quasi-periodic bifurcation theory

Invariant tori with quasi-periodic dynamics often allow to better
understand the behaviour of a dynamical system. Their complexity
ranges between equilibria and periodic orbits on the one side and
more complicated structures of dynamics like strange attractors
on the other side.

To capture the dynamics on quasi-periodic tori one should introduce
parameters; both tori with dense orbits and completely resonant
tori consisting of periodic orbits correspond to dense subsets of
the parameter space. Under variation of parameters bifurcations
can occur.

In dissipative dynamical systems the parameters are external (e.g.
think of the Reynolds number, then repeated Hopf bifurcations might
explain the onset of turbulence) while in Hamiltonian systems the
parameters are the actions conjugate to the toral angles. Other
contexts to which the theory applies include volume-preserving and
reversible systems.