Reducible problem for a class of almost-periodic non-linear Hamiltonian systems

This paper studies the reducibility of almost-periodic Hamiltonian systems with small perturbation near the equilibrium which is described by the following Hamiltonian system: dx/dt = J [A +εQ(t,ε) ]x+ ε g(t,ε)+h(x,t,ε). It is proved that, under some non-resonant conditions, non-degeneracy conditions, the suitable hypothesis of analyticity and for the sufficiently small ε , the system can be reduced to a constant coefficients system with an equilibrium by means of an almost-periodic symplectic transformation.