  Maximum entropy principle does not seem to distinguish between the use of
Tsallis and Renyi entropies as either of them may be used to derive similar
power-law distributions. In this paper, we address the question whether the
Renyi entropy is equally suitable to describe those systems with power-law
behaviour, where the use of the Tsallis entropy is relevant. We discuss a
specific class of dynamical systems, namely, one dimensional dissipative maps
at chaos threshold and make our study from two aspects: i) power-law
sensitivity to the initial conditions and the rate of entropy increase, ii)
generalized bit cumulants. We present evidence that the Tsallis entropy is the
more appropriate entropic form for such studies as opposed to Renyi form.
