3 papers
math.DS2025
Averaging method for quasi-periodic response solutions
Jiamin Xing, Yong Li, Shuguan Ji
In this paper, we present an averaging method for obtaining quasi-periodic response solutions in perturbed, real analytic, quasi-periodic systems with Diophantine frequency vectors…
math.DS2023
Lower dimensional invariant tori for multi-scale Hamiltonian systems
Weichao Qian, Shuguan Ji, Yong Li
The ``Fundamental Theorem" given by Arnold in [2] asserts the persistence of full dimensional invariant tori for 2-scale Hamiltonian systems. However, persistence in multi-scale sy…
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…