In this paper we consider the persistence of elliptic lower-dimensional invariant tori
with prescribed frequencies in Hamiltonian systems with small parameters. Under the Brjuno
nondegeneracy condition, if the prescribed frequencies satisfy a Diophantine condition, by the
KAM technique we prove that for most of small parameters in the sense of Lebesgue measure,
the Hamiltonian systems admit a lower-dimensional invariant torus whose frequency vector is
a dilation of the prescribed frequencies.
Keywords:
Hamiltonian system, invariant tori, KAMiteration, Brjuno nondegeneracy condition
Citation:
Zou H., Xu J., On Elliptic Lower-Dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems with Small Parameters, Regular and Chaotic Dynamics,
2024, Volume 29, Number 4,
pp. 583-604