Heinz Hanßmann, Carles Simó
Dynamical stability of quasi-periodic response solutions
in planar conservative systems
(2488K, PostScript)
ABSTRACT. We study non-autonomous planar Hamiltonian
or reversible vector fields that vanish at the origin.
The time-dependence is quasi-periodic with strongly
non-resonant frequencies. First we give a simple criterion
in terms of the averaged system for the trivial solution
to be dynamically stable. Then we obtain destabilizations
for classes of examples where the conditions of the
criterion are not satisfied. We end with possible ways
to stabilize an unstable trivial solution by means of
vector fields with zero average.