On the computation of the entropy for dissipative maps at the edge of chaos using non-extensive statistical mechanics

Tsallis' non-extensive statistical mechanics is claimed to be the correct tool to describe the behaviour of low-dimensional dissipative maps at the edge of chaos. Indeed, many different approaches confirm that, for those systems, the evolution is governed by power-laws, not exponential, trends; this coincides with predictions from generalized thermostatistics. In this work, however, we present some analytical considerations, supported also by some simple numerical examples, suggesting the existence of contradictions within this picture.