  The quasi-periodic homogenization for some classes of first-order
Hamilton-Jaconi-Bellman equation is studied in this paper. The cell problem of
the quasi-periodic homogenization satisfies the non-resonance condition, under
which the corresponding deterministic system is ergodic. The almost periodic
homogenization for the same classes of equations is also solved, as a limit of
a sequence of quasi-periodic homogenizations. Here, the almost periodicity is
in the sense of H. Bohr. This result has been cited by some authors, for
example: by H. Ishii, "Almost periodic homogenization of Hamilton-Jacobi
equations", in Int. Conf. on Diff. Eqs., vol.1, Berlin, 1999, World Scientific,
River Edge, NJ 2000, pp. 600-605; and by P.-L. Lions, and P.E. Souganidis,
"Correctors for the Homogenizations of Hamilton-Jacobi Equations in the
stationary ergodic setting", Comm. Pure Appl. Math. LVI, (2003), pp. 1501-1524.
