KAM Type-Theorem for Lower Dimensional Tori in Random Hamiltonian Systems (Communications in Mathematical Research, 2021)
In this paper, we study the persistence of lower dimensional tori for random Hamiltonian systems, which shows that majority of the unperturbed tori persistas Cantor fragments of lower dimensional ones under small perturbation. Using thisresult, we can describe the stability of the non-autonomous dynamic systems.
Keywords: random Hamiltonian system; KAM type theorem; Cantor fragment of invariant tori.