We consider the following real two-dimensional nonlinear analytic quasi-periodic Hamiltonian system , where with and as . Without any nondegeneracy condition with respect to ε, we prove that for most of the sufficiently small ε, by a quasi-periodic symplectic transformation, it can be reduced to a quasi-periodic Hamiltonian system with an equilibrium.
Jia Li. Junxiang Xu. "On the Reducibility for a Class of Quasi-Periodic Hamiltonian Systems with SmallPerturbation Parameter." Abstr. Appl. Anal. 2011 (SI1) 1 - 17, 2011. https://doi.org/10.1155/2011/354063