4 papers · 1 filter
Persistence of invariant graphs for twist maps under analytic perturbations
Qi Li, Yi Liu, Lin Wang
We construct high-frequency perturbations of an integrable exact symplectic twist map which preserve an analytic invariant graph with a prescribed rotation number. Their oscillatio…
Herman's converse KAM mechanism revisited
Yi Liu, Lin Wang
In his celebrated counterexample to the KAM theorem, Herman introduced a perturbation of an integrable system consisting of two components: a hyperbolic term and a bump function. H…
On Non-KAM Invariant Circles for Area-Preserving Twist Maps
Jiashen Guo, Yi Liu, Lin Wang
In this note, we investigate the dynamics of invariant circles in area-preserving twist maps. The invariant circles under consideration lie beyond the applicability of classical KA…
Moser's twist theorem revisited
Yi Liu, Lin Wang
Inspired by the work of Katznelson and Ornstein, we present a short way to achieve the almost optimal regularity in Moser's twist theorem. Specifically, for an integrable area-pres…