Quantitative KAM theory, with an application to the three-body problem
Dynamical Systems
2024-07-10 v2 Mathematical Physics
math.MP
Abstract
Based on quantitative ``{\sc kam} theory'', we state and prove two theorems about the continuation of maximal and whiskered quasi--periodic motions to slightly perturbed systems exhibiting proper degeneracy. Next, we apply such results to prove that, in the three--body problem, there is a small set in phase space where it is possible to detect both such families of tori. We also estimate the density of such motions in proper ambient spaces. Up to our knowledge, this is the first proof of co--existence of stable and whiskered tori in a physical system.
Cite
@article{arxiv.2302.00279,
title = {Quantitative KAM theory, with an application to the three-body problem},
author = {Gabriella Pinzari and Xiang Liu},
journal= {arXiv preprint arXiv:2302.00279},
year = {2024}
}
Comments
{\bf Key-words:} Properly-degenerate Hamiltonian, symplectic coordinates, symmetry reductions. 34 pages, 2 figures