Nils BERGLUND

Institut de Physique Théorique
EPFL, PHB-Ecublens
CH-1015 Lausanne
Switzerland
berglund@iptsg.epfl.ch

Invariant manifolds and Nekhoroshev estimates in adiabatic dynamical systems

Abstract: We consider n-dimensional adiabatic dynamical systems of the form epsilon dx/dt = f(x,t). We prove existence of linear and nonlinear invariant manifolds near hyperbolic fixed points. These manifolds admit asymptotic series in the adiabatic parameter epsilon, which can be truncated in such a way that they approach these manifolds exponentially closely.