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24 June 2024
 
  » arxiv » 2302.00279

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Quantitative KAM theory, with an application to the three-body problem
Gabriella Pinzari ; Xiang Liu ;
Date 1 Feb 2023
AbstractBased 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.
Source arXiv, 2302.00279
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