Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774211 | Journal of Differential Equations | 2017 | 24 Pages |
Abstract
Let f be an exact area-preserving monotone twist diffeomorphism of the infinite cylinder and PÏ,f(ξ) be the associated Peierls barrier. In this paper, we give the Hölder regularity of PÏ,f(ξ) with respect to the parameter f. In fact, we prove that if the rotation symbol Ïâ(RâQ)â(Q+)â(Qâ), then PÏ,f(ξ) is 1/3-Hölder continuous in f, i.e.|PÏ,fâ²(ξ)âPÏ,f(ξ)|â¤Câfâ²âfâC11/3,âξâR where C is a constant. Similar results also hold for the Lagrangians with one and a half degrees of freedom. As application, we give an open and dense result about the breakup of invariant circles.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Qinbo Chen, Chong-Qing Cheng,