n-1 Independent First Integrals for Linear Differential Systems in R^n and C^n

Manuel Falconi & Jaume Llibre

Dedicated to Jorge Sotomayor on his 60th birthday

We prove that every linear system with constant coefficients on $\R^n$ or $\C^n$ is Darboux integrable by providing a complete explicit list of $n-1$ independent Darboux first integrals.