TY - JOUR
T1 - A KAM-Type Theorem for Generalized Hamiltonian Systems
AU - Liu , Baifeng
AU - Zhu , Wenzhuang
AU - Xu , Leshun
JO - Communications in Mathematical Research 
VL - 1
SP - 37
EP - 52
PY - 2021
DA - 2021/05
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19181.html
KW - KAM theory, invariant tori, generalized Hamiltonian system.
AB - <p style="text-align: justify;">In this paper we mainly concern the persistence of lower-dimensional
invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian
systems refer to the systems which may admit a distinct number of action and angle
variables. In particular, system under consideration can be odd dimensional. Under
the Rüssmann type non-degenerate condition, we proved that the majority of the
lower-dimension invariant tori of the integrable systems in generalized Hamiltonian
system are persistent under small perturbation. The surviving lower-dimensional tori
might be elliptic, hyperbolic, or of mixed type.</p>