Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900118 | Journal of Mathematical Analysis and Applications | 2018 | 39 Pages |
Abstract
In this paper, we will focus on the persistence of elliptic-type degenerate invariant tori with the same frequency vector ÏâRd as the forcing in a class of quasi-periodically forced four-dimensional non-conservative systems. It is shown that, under suitable hypothesis of smoothness with respect to ϵ and the Brjuno-Rüssmann's non-resonant condition instead of ordinary Diophantine condition with respect to the frequency vector ÏâRd, the invariant tori persist under small perturbations for most of the sufficiently small parameters ϵ in the sense of the Lebesgue measure. Hence, the system has a quasi-periodic solution with the same frequency vector Ï as the forcing. The proof is based on the Pöschel-Rüssmann KAM method, which is a KAM-type method in which one uses the polynomial structure of function to truncate, introduce a parameter q and make the steps of KAM iteration infinitely small in the speed of function qnκ,0
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Wen Si, Jianguo Si,