Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps

The sensitivity to initial conditions and the entropy production per unit time of one-dimensional dissipative maps were investigated. Ensemble averages were made by sampling randomly the entire phase space. One dimensional dissipative maps referred to as exponential maps are introduced to have one more paradigmatic universality class on which basic properties could be tested. The results led to the numerical confirmation, for the standard logistic maps and one dimensional dissipative maps, of an appropriate generalization of the Pesin identity.