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math.DS2023
An Infinite-dimensional KAM Theorem with Normal Degeneracy
Jiayin Du, Lu Xu, Yong Li
In this paper, we consider a classical Hamiltonian normal form with degeneracy in normal direction. In previous results, one needs to assume that the perturbation satisfies certain…
math.DS2023
Melnikov's persistence for completely degenerate Hamiltonian systems
Jiayin Du, Shuguan Ji, Yong Li
In this paper, we study the Melnikov's persistence for completely degenerate Hamiltonian systems with the following Hamiltonian \begin{equation*} H(x,y,u,v)=h(y)+g(u,v)+\varepsilon…
math.DS2022★ 2 cited
Kolmogorov's Theorem for Degenerate Hamiltonian Systems with Continuous Parameters
Jiayin Du, Yong Li, Hongkun Zhang
In this paper, we investigate Kolmogorov type theorems for small perturbations of degenerate Hamiltonian systems. These systems are index by a parameter as \( H(y,x,ξ) = \langl…