3 papers
math.DS2025
The multi-scale KAM persistence without a scaling order for Hamiltonian systems
Weichao Qian, Yong Li, Xue Yang
The persistence of invariant tori in multi-scale Hamiltonian systems is intrinsically linked to the stability of the N-body problem. However, the existing non-degeneracy conditions…
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
KAM Theorems for Multi-scale Torus
Weichao Qian, Yixian Gao, Yong Li
In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulu…