The following system:

is considered, where Ais a constant matrix with eigenvalues of different real parts, and  is quasi-periodic with frequencies  Suppose that  has continuous partial derivatives  for    (τ relates with the Diophantine condition) and  and the moduli of continuity of  satisfy a condition of finiteness (condition on an integral), which is more general than a Hölder condition. Then for sufficiently small  by a quasi-periodic homeomorphism, the system can be reducible to a constant coefficient differentiable equation.

reducibility, finitely differentiable, quasi-periodic.