Heinz Hanßmann
A Survey on Bifurcations of Invariant Tori
(127K, PostScript, gzipped and uuencoded)
ABSTRACT. Invariant tori of dynamical systems occur both in
the dissipative and in the conservative context. I focus here
on the latter, where the tori are intrinsically parametrised
by the actions $\, y_1, \ldots, y_n \,$ conjugate to the angles
$\, x_1, \ldots, x_n \,$ on the torus. The distribution of
maximal tori in a nearly integrable Hamiltonian system is
governed by the invariant tori of co--dimension one. The
different Cantor families of maximal tori shrink down to
normally elliptic tori and are separated by the web formed by
stable and unstable manifolds of normally hyperbolic tori.
The lower dimensional invariant tori form Cantor families
themselves, and occurring bifurcations in turn organize the
distribution of normally elliptic and hyperbolic tori.