Lyapunov exponents of solutions to linear differential equations with periodic forcing functions

We give Lyapunov exponents of solutions to linear differential equations of the form x = Ax + f (t), where A is a complex matrix and f (t) is a τ -periodic continuous function. Notice that f (t) is not “small” as t→∞. The proof is essentially based on a representation [J. Kato, T. Naito, J.S. Shin, A characterization of solutions in linear differential equations with periodic forcing functions, J. Difference Equ. Appl. 11 (2005) 1–19] of solutions to the above equation. © 2008 Elsevier Inc. All rights reserved.