The other day I saw a new mom with a 5-week-old baby who spent a good part of his day crying. The mom had done the things moms with babies who cry a lot often do: she had blamed something in her breast milk and stopped breastfeeding, then she had started working her way through the various infant formulas in the grocery store; still her baby would not stop crying. “He looks like he’s in pain. H...

1. Introduction How to look at a dynamical system f at a small scale? You should take a small piece of the phase space, consider the rst return map to this piece, and then rescale it to \the original size". The new dynamical system is called the renormalization Rf of the original one. It may happen that Rf looks \similar" to f, and then you can try to repeat this procedure, and construct the se...