Exponential wealth distribution : a new approach from functional iteration theory

Different approaches are possible in order to derive the exponential regime in statistical systems. Here, a new functional equation is proposed in an economic context to explain the wealth exponential distribution. Concretely, the new iteration [1] given by \begin{equation} f_{n+1}(x) = \int\!\!\int_{u+v>x}\,{f_n(u)f_n(v)\over u+v} \; {\mathrm d}u{\mathrm d}v \,. \nonumber \label{syst1} \end{equation