57 citations · 203 across the 13 of their papers we have counts for
14 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…
On the relativistic Lagrange-Laplace secular dynamics for extrasolar systems
M. Sansottera, L. Grassi, A. Giorgilli
We study the secular dynamics of extrasolar planetary systems by extending the Lagrange-Laplace theory to high order and by including the relativistic effects. We investigate the l…
A Kepler's note on secular inequalities
Antonio Giorgilli
I discuss the problem of secular inequalities in Kepler by giving account of a manuscript note that has not been published until 1860. In his note Kepler points out the need for a…
Normal Form and Energy Conservation of High Frequency Subsystems Without Nonresonance Conditions
Dario Bambusi, Antonio Giorgilli, Simone Paleari +1
We consider a system in which some high frequency harmonic oscillators are coupled with a slow system. We prove that up to very long times the energy of the high frequency system c…
On the convergence of an algorithm constructing the normal form for lower dimensional elliptic tori in planetary systems
Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normali…