2014/01/25 by Antonio Giorgilli, Giorgilli, Antonio, Ugo Locatelli +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum chaos and dynamical systems #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1401.6529
45 pages
arxiv created 2014/01/25 · arxiv updated 2014/01/28
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 normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytical work in our previous article (2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies.