  We show that certain linear elliptic equations (and systems) in divergence
form with almost periodic coefficients have bounded, almost periodic
correctors. This is proved under a new condition we introduce which quantifies
the almost periodic assumption and includes (but is not restricted to) the
class of smooth, quasiperiodic coefficient fields which satisfy a
Diophantine-type condition previously considered by Kozlov. The proof is based
on a quantitative ergodic theorem for almost periodic functions combined with
the new regularity theory recently introduced by the first author and Shen for
equations with almost periodic coefficients. This yields control on spatial
averages of the gradient of the corrector, which is converted into estimates on
the size of the corrector itself via a multiscale Poincar\'e-type inequality.
