Kolmogorov variation: KAM with knobs (à la Kolmogorov)
arXiv:2109.06345
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 (10)
- A lecture on the classical KAM theorem
- Twistless KAM tori
- Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review
- Kolmogorov and Nekhoroshev theory for the problem of three bodies
- Energy localization on q-tori, long term stability and the interpretation of FPU recurrences
- On the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system
- On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems
- Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
- Low-dimensional q-Tori in FPU Lattices: Dynamics and Localization Properties
- On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori