  We introduce an interesting hierarchy of rational order chaotic maps that
posses an invariant measure. In contrast to the previously introduced hierarchy
of chaotic maps \cite{J1,J2,J3,J4,J5}, with merely entropy production, the
rational order chaotic maps can simultaneously produce and consume entropy . We
compute the Kolmogorov-Sinai entropy of theses maps analytically and also their
Lyapunov exponent numerically, where that obtained numerical results support
the analytical calculations.
