A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems

We describe a method to study the existence ofwhiskered quasi-periodic solutions in Hamiltoniansystems.The method applies to finite dimensional systemsand also to lattice systems and to PDE's includingsome ill posed ones.In coupled map lattices, we can alsoconstruct solutions of infinitely many frequencieswhich do not vanish asymptotically.