as being a “generic” solution. However, in the mathematics literature the word “generic” is restricted to describing either an open dense subset of the set of all solutions, or (when this can be defined) a subset of measure unity of the set of all solutions. In this work we shall stick to the mathematical terminology. We shall have nothing rigorous to say about whether our general solution is also generic. However, we wish to emphasize the following points.

First, let us mention that the set $V$ of solutions to the velocity-dominated equations that are asymptotic to solutions of the complete equations is not identical to the set $U$ of all solutions to the velocity-dominated constraint equations. The subset $V \subset U$ is defined by imposing some inequalities on the free data. These inequalities do not change the number of free functions. Therefore the solutions in $V$ are still “general”. One can wonder whether there could be a co-existing general behaviour, corresponding to initial data that do not fulfill the inequalities. For instance, could such “bad” initial data lead to a generalized mixmaster regime? This is a difficult question and we shall only summarize here what is the existing evidence. There 