Fractional Lindstedt series

Lindstedt Series and Kolmogorov Theorem

the KAM theorem from a combinatorial viewpoint. Lindstedt, Newcomb and Poincaré introduced a remarkable trigonometric series motivated by the analysis of the three body problem, [P]. In modern language, [G2], it is the generating function, that I call Lindstedt series here, ~h(~ ψ) = ∑∞ k=1 ε k~h(k)(~ ψ) of the sequence ~h(k)(~ ψ) of trigonometric polynomials associated with well known combinat...

Lindstedt Series, Ultraviolet Divergences and Moser's Theorem

Moser's invariant tori for a class of nonanalytic quasi integrable even hamiltonian systems are shown to be analytic in the perturbation parameter. We do so by exhibiting a summation rule for the divergent series (\Lindstedt series") that formally deene them. We nd additional cancellations taking place in the formal series, besides the ones already known and necessary in the analytic case (i.e....

Lindstedt Series for Lower Dimensional Tori

Lindstedt series for perturbations of isochronous systems. I. General theory

Abstract. We give a proof of the persistence of invariant tori for analytic perturbations of isochronous systems by using the Lindstedt series expansion for the solutions. With respect to the case of anisochronous systems, there is the additional problem to find the set of allowed rotation vectors for the invariant tori, which can not given a priori simply by looking at the unperturbed system, ...

Lindstedt Series Solutions of the Fermi-Pasta-Ulam Lattice

We apply the Lindstedt method to the one dimensional Fermi-Pasta-Ulam β lattice to find fully general solutions to the complete set of equations of motion. The pertubative scheme employed uses ǫ as the expansion parameter, where ǫ is the coefficient of the quartic coupling between nearest neighbors. We compare our non-secular perturbative solutions to numerical solutions and find striking agree...