57 citations · 111 across the 6 of their papers we have counts for
6 papers
Improved convergence estimates for the Schröder-Siegel problem
Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
We reconsider the Schröder-Siegel problem of conjugating an analytic map in in the neighborhood of a fixed point to its linear part, extending it to the case of dimens…
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…
Methods of algebraic manipulation in perturbation theory
Antonio Giorgilli, Marco Sansottera
We give a short introduction to the methods of representing polynomial and trigonometric series that are often used in Celestial Mechanics. A few applications are also illustrated.
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…
On a theorem of Lyapounov
Antonio Giorgilli
It is shown that a Hamiltonian system in the neighbourhood of an equilibrium may be given a special normal form in case the eigenvalues of the linearized system satisfy non--resona…
On the representation of maps by Lie transforms
Antonio Giorgilli
The problem of representing a class of maps in a form suited for application of normal form methods is revisited. It is shown that using the methods of Lie series and of Lie transf…