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  1. Article

    Open Access

    Existence proof of librational invariant tori in an averaged model of HD60532 planetary system

    We investigate the long-term dynamics of HD60532, an extrasolar system hosting two giant planets orbiting in a 3:1 mean motion resonance. We consider an average approximation at order one in the masses which r...

    Veronica Danesi, Ugo Locatelli… in Celestial Mechanics and Dynamical Astronomy (2023)

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  2. No Access

    Article

    A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems

    The inclinations of exoplanets detected via radial velocity method are essentially unknown. We aim to provide estimations of the ranges of mutual inclinations that are compatible with the long-term stability o...

    Mara Volpi, Ugo Locatelli, Marco Sansottera in Celestial Mechanics and Dynamical Astronomy (2018)

  3. No Access

    Article

    Rigorous estimates for the relegation algorithm

    We revisit the relegation algorithm by Deprit et al. (Celest. Mech. Dyn. Astron. 79:157–182, 2001) in the light of the rigorous Nekhoroshev’s like theory. This relatively recent algorithm is nowadays widely used ...

    Marco Sansottera, Marta Ceccaroni in Celestial Mechanics and Dynamical Astronomy (2017)

  4. No Access

    Article

    On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems

    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 the case of...

    Antonio Giorgilli, Ugo Locatelli… in Celestial Mechanics and Dynamical Astronomy (2014)

  5. No Access

    Article

    Effective stability around the Cassini state in the spin-orbit problem

    We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay variables...

    Marco Sansottera, Christoph Lhotka… in Celestial Mechanics and Dynamical Astronomy (2014)

  6. No Access

    Article

    On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems

    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 variables, we...

    Anne-Sophie Libert, Marco Sansottera in Celestial Mechanics and Dynamical Astronomy (2013)

  7. No Access

    Article

    A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems

    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 elliptic torus...

    Marco Sansottera, Ugo Locatelli… in Celestial Mechanics and Dynamical Astronomy (2011)

  8. No Access

    Article

    Kolmogorov and Nekhoroshev theory for the problem of three bodies

    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 perturbation e...

    Antonio Giorgilli, Ugo Locatelli… in Celestial Mechanics and Dynamical Astronomy (2009)