4 papers
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…
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…
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…
Quasiperiodic Poincare Persistence at High Degeneracy
Weichao Qian, Yong Li, Xue Yang
For Hamiltonian systems with degeneracy of any higher order, we study the persistence of resonant invariant tori, which as some lower-dimensional invariant tori might be elliptic,…