Article ID Journal Published Year Pages File Type
5774211 Journal of Differential Equations 2017 24 Pages PDF
Abstract
Let f be an exact area-preserving monotone twist diffeomorphism of the infinite cylinder and Pω,f(ξ) be the associated Peierls barrier. In this paper, we give the Hölder regularity of Pω,f(ξ) with respect to the parameter f. In fact, we prove that if the rotation symbol ω∈(R∖Q)⋃(Q+)⋃(Q−), then Pω,f(ξ) is 1/3-Hölder continuous in f, i.e.|Pω,f′(ξ)−Pω,f(ξ)|≤C‖f′−f‖C11/3,∀ξ∈R 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
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