Quasiperiodic Poincare Persistence at High Degeneracy
Dynamical Systems
2023-11-07 v2
Abstract
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, hyperbolic or of mixed types. Hence we prove a quasiperiodic Poincare theorem at high degeneracy. This answers a long standing conjecture on the persistence of resonant invariant tori in quite general situations.
Keywords
Cite
@article{arxiv.2111.11619,
title = {Quasiperiodic Poincare Persistence at High Degeneracy},
author = {Weichao Qian and Yong Li and Xue Yang},
journal= {arXiv preprint arXiv:2111.11619},
year = {2023}
}