  The aim of this paper is to show that the invariant measure for a class of
one dimensional chaotic maps, $T(x)$, is an extended solution of the Schr\"oder
functional equation, $q(T(x))=\lambda q(x)$, induced by them. Hence, we give an
unified treatment of a collection of exactly solved examples worked out in the
current literature. In particular, we show that these examples belongs to a
class of functions introduced by Mira, (see text). Moreover, as a new example,
we compute the invariant densities for a class of rational maps having the
Weierstrass $\wp$ functions as an invariant one. Also, we study the relation
between that equation and the well known Frobenius-Perron and Koopman's
operators.
