Ph. Chartier, A. Murua and J.M. Sanz-Serna, Higher-order averaging, formal series and numerical integration II: the quasi-periodic case, Found. Comput. Maths. 12(2012), 471-508. See next item. IN THE PDF BELOW WE HAVE REMOVED THE MISPRINTS OF THE ORIGINALLY PUBLISHED PAPER THAT ARE OUTLINED IN THE ERRATUM.