  The aim of this manuscript is to understand the dynamics of products of
nonnegative matrices. We extend a well known consequence of the
Perron-Frobenius theorem on the periodic points of a nonnegative matrix to
products of finitely many nonnegative matrices associated to a word and later
to products of nonnegative matrices associated to a word, possibly of infinite
length. We also make use of an appropriate definition of the exponential map
and the logarithm map on the positive orthant of $\mathbb{R}^{n}$ and explore
the relationship between the periodic points of certain subhomogeneous maps
defined through the above functions and the periodic points of matrix products,
mentioned above.
