  We perform a throughout numerical study of the average sensitivity to initial
conditions and entropy production for two symplectically coupled standard maps
focusing on the control-parameter region close to regularity. Although the
system is ultimately strongly chaotic (positive Lyapunov exponents), it first
stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue
that the nonextensive generalization of the classical formalism is an adequate
tool in order to get nontrivial information about this complex phenomenon.
Within this context we analyze the relation between the power-law sensitivity
to initial conditions and the entropy production.
