Large Dynamical stability of quasi-periodic response solutions in planar
conservative systems}

Heinz Han{\ss}mann
Mathematisch Instituut, Universiteit Utrecht,
Postbus~80.010, 3508~TA Utrecht, The~Netherland

Carles Sim\'o
Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona
Gran Via 585, 08007 Barcelona, Spain}}

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.