KAM persistence for multiscale generalized Hamiltonian systems
Weichao Qian, Yang Xue, Yong Li · Communications in Mathematical Sciences · 2023
This paper concerns the persistence of invariant tori for multiscale generalized Hamiltonian systems.A multiscale nondegenerate condition on Poisson manifold comparing Kolmogorov nondegenerate one on symplectic manifold and multiscale iso-energetically nondegenerate condition on Poisson manifold comparing iso-energetically nondegenerate one due to Arnold are introduced, hence some multiscale KAM theorems and multiscale iso-energetic KAM theorems on Poisson manifold are established.And we give three applications by a direct example, first order PDEs and steady Euler fluid path flow, respectively.