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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.DS2020
Anderson Localization for Long-Range operators with Singular Potentials
Wenwen Jian, Jia Shi, Xiaoping Yuan
In this paper, we use Cartan estimate for meromorphic functions to prove Anderson localization for a class of long-range operators with singular potenials.
math.DS2019
Anderson localization for the Maryland model with long range interactions
Jia Shi, Xiaoping Yuan
In this paper, we establish Anderson localization for the Maryland model with long range interactions.