  We show that the dynamical and entropic properties at the chaos threshold of
the logistic map are naturally linked through the nonextensive expressions for
the sensitivity to initial conditions and for the entropy. We corroborate
analytically, with the use of the Feigenbaum renormalization group(RG)
transformation, the equality between the generalized Lyapunov coefficient
$\lambda_{q}$ and the rate of entropy production $K_{q}$ given by the
nonextensive statistical mechanics. Our results advocate the validity of the
$q$-generalized Pesin identity at critical points of one-dimensional nonlinear
dissipative maps.
