Kolmogorov variation: KAM with knobs (à la Kolmogorov)

Abstract

In this paper we reconsider the original Kolmogorov normal form algorithm with a variation on the handling of the frequencies. At difference with respect to the Kolmogorov approach, we do not keep the frequencies fixed along the normalization procedure. Besides, we select the frequencies of the final invariant torus and determine a posteriori the corresponding starting ones. In particular, we replace the classical translation step with a change of the frequencies. The algorithm is based on the original scheme of Kolmogorov, thus exploiting the fast convergence of the Newton-Kantorovich method.

References in corpus (4)

• A lecture on the classical KAM theorem
• Kolmogorov and Nekhoroshev theory for the problem of three bodies
• Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
• On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori

Cited by in corpus (1)

• Normal form for lower dimensional elliptic tori in Hamiltonian systems