@ARTICLE{gaubert96a, author={S. Gaubert}, title={On semigroups of matrices in the $(\max,+)$ algebra}, journal={Semigroup Forum}, year={1996}, note={to appear. Preliminary version: Rapport INRIA Number 2172 (Jan. 1994)}, }

We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max,+)-algebra (that is, the semiring $(R\cup\{-\infty\},\max,+)$), and also for semigroups of (max,+)-linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed.