57 citations · 143 across the 7 of their papers we have counts for
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Invariant KAM tori: from theory to applications to exoplanetary systems
Ugo Locatelli, Chiara Caracciolo, Marco Sansottera +1
We consider the classical problem of the construction of invariant tori exploiting suitable Hamiltonian normal forms. This kind of approach can be translated by means of the Lie se…
Computer-assisted estimates for Birkhoff normal forms
Chiara Caracciolo, Ugo Locatelli
Birkhoff normal forms are commonly used in order to ensure the so called "effective stability" in the neighborhood of elliptic equilibrium points for Hamiltonian systems. From a th…
Elliptic tori in FPU non-linear chains with a small number of nodes
Chiara Caracciolo, Ugo Locatelli
We revisit an algorithm constructing elliptic tori, that was originally designed for applications to planetary hamiltonian systems. The scheme is adapted to properly work with mode…
Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach fir…
Kolmogorov and Nekhoroshev theory for the problem of three bodies
Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
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…