Degenerate fixed points of maps in Banach spaces and lattices with decay and their invariant manifolds

Degenerate fixed points of maps appear in many interesting problems in Celestial Mechanics, Economics and Chemistry. Lattice systems, that is, dynamical systems consisting in an infinite array of finite dimensional subsystems interacting locally among them appear in many models of Biology, Physics and Mathematics. In this work, we extend the results concerning the existence of stable and unstable invariant manifolds of degenerate fixed points to lattice systems with decay properties. As an example, we find such manifolds in perturbations of the Toda lattice.