In this contribution to the volume in memoriam of Michel Henon, we thought appropriate to look at his early scientific work devoted to the dynamics of large assemblies of interacting masses. He predicted in his PhD thesis that, in such a system, firs
t a collapse of mass occurs at the center and that later binaries stars are formed there. Henceforth, the negative energy of binding of pairs becomes a source of positive energy for the rest of the cluster which evaporate because of that. We examine under what conditions such a singularity can occur, and what could happen afterwards. We hope to show that this fascinating problem of evolution of self-gravitating clusters keeps its interest after the many years passed since Henon thesis, and is still worth discussing now.
An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of money has recently been proposed by one of us (RLR). This equation takes the form of an iterated
nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.
