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math.DS2022
Resonances and Phase Locking Phenomena for Foliation Preserving Torus Maps
Xiaolong He, Rafael de la Llave
It is well known for experts that resonances in nonlinear systems lead to new invariant objects that lead to new behaviors. The goal of this paper is to study the invariant sets ge…
math.DS2020★ 1 cited
On linear stability of KAM tori via the Craig-Wayne-Bourgain method
Xiaolong He, Jia Shi, Yunfeng Shi +1
In this paper, we prove the Melnikov's persistency theorem by combining the traditional Kolmogorov-Arnold-Moser (KAM) technique and the Craig-Wayne-Bourgain (CWB) method. The aim o…
math.DS2018★ 1 cited
Construction of quasi-periodic solutions for delayed perturbation differential equations
Xiaolong He, Xiaoping Yuan
We employ the Craig-Wayne-Bourgain method to construct quasi-periodic solutions for delayed perturbation differential equations. Our results not only implement the existing literat…