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

Abstract

AbstractWe 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