  The sensitivity to initial conditions and relaxation dynamics of
two-dimensional maps are analyzed at the edge of chaos, along the lines of
nonextensive statistical mechanics. We verify the dual nature of the entropic
index for the Henon map, one ($q_{sen}<1$) related to its sensitivity to
initial conditions properties, and the other, graining-dependent
($q_{rel}(W)>1$), related to its relaxation dynamics towards its stationary
state attractor. We also corroborate a scaling law between these two indexes,
previously found for $z$-logistic maps. Finally we perform a preliminary
analysis of a linearized version of the Henon map (the smoothed Lozi map). We
find that the sensitivity properties of all these $z$-logistic, Henon and Lozi
maps are the same, $q_{sen}=0.2445...$
