a1 Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124, U.S.A.
Suppose the linear equation x' = A(t)x has an exponential dichotomy and suppose B(t) is close to A(t) in the following sense: on any interval of length 2T, B(t) is close to some translate A(t + τ) of A(t) (actually the conditions in the paper are slightly weaker than this). Then if T is sufficiently large, the equation y' = B(t)y also has an exponential dichotomy. This generalises the usual roughness theorem for exponential dichotomies.
(Received July 23 1986)