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We show that the dynamical and entropic properties at the chaos threshold ofthe logistic map are naturally linked through the nonextensive expressions forthe sensitivity to initial conditions and for the entropy. We corroborateanalytically, 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 thenonextensive statistical mechanics. Our results advocate the validity of the$q$-generalized Pesin identity at critical points of one-dimensional nonlineardissipative maps.Comment: Revtex, 5 pages, 3 figure

Nonextensive Pesin identity: Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map