… parameterization method”, a technique recently introduced by the authors [CFdlL03a,CFdlL03b]
to study invariant manifolds … K as giving a parameterization of the invariant manifold K(U1…

… parameterization method”, a technique recently introduced by the authors [CFdlL03a, CFdlL03b]
to study invariant manifolds … as giving a parameterization of the invariant manifold K(U1)…

… As a first application, we consider the dynamical system given by a Cr … Introduction and
statements of results … that are called Sylvester equations in [3]. One of the advantages of the …

… manifold in a simple finite dimensional example. In Sect. 3 we extend the parameterization
method to a … A complete overview of the literature is beyond the scope of the present brief …

… Three features of the method are that (1) we obtain accurate … and we attempt only a brief
overview. Our primary objective is … Another important application of the parameterization method …

… approach to invariant manifolds of periodically-perturbed vector fields about a periodic orbit
with the same frequency, with a direct application … As previously noticed, it uses purely three-…

… We will offer a rather complete review of the application of the parameterization method for
invariant tori in quasi-periodic systems in Chapter 3, including a detailed version of a Newton-…

… We also discuss an application of this framework to the … more complete overview of the
various notions of the slow manifold we … In Section 3 we develop a power series formalism for the …

… understanding the application of the parameterization method for invariant … summary, the
reduced model accurately identified the internal resonances. At point b, there is a significant 1:3 …

… of parabolic invariant manifolds in R2 and applications to Celestial Mechanics. … introduced
recently in [2, 3, 4]. In this … We give an overview of the method in Section 2. The solution of the …