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We consider a one-dimensional discrete nonlinear Schr{\"o}dinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift… (More)

We study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincaré canonical… (More)

We adapt the Kolmogorov’s normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant… (More)

We investigate the long time stability in Nekhoroshev’s sense for the Sun– Jupiter–Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge… (More)

We reconsider the Schröder–Siegel problem of conjugating an analytic map in $$\mathbb {C}$$C in the neighborhood of a fixed point to its linear part, extending it to the case of dimension $$n>… (More)

Abstract We revisit the problem of introducing an a priori control for devices that can be modeled via a symplectic map in a neighborhood of an elliptic equilibrium. Using a technique based on Lie… (More)

We consider a 1-dimensional discrete nonlinear Schr\"odinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence of phase-shift discrete solitons, which… (More)

We give a constructive proof of the existence of elliptic lower dimensional tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov normalization algorithm to… (More)

We adapt the Kolmogorov’s normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant… (More)

La teoria di Lagrange per i moti secolari delle eccentricit\`a ed
inclinazioni delle orbite planetarie si fondava su
un\:approssimazione, dettata in larga misura dalla complessit\`a dei
calcoli… (More)