The metallic means family and renormalization group techniques

We present the new family of Metallic Means (MMF), being the most paramount of its members, the Golden Mean $\phi$ and, in the second place, the Silver Mean $\sigma_{Ag}$. Why do we call them a family? Because, besides carrying the name of a metal–the Golden Mean, the Silver Mean, the Copper Mean, the Bronze Mean, the Nickel Mean–they enjoy common mathematical properties that attach a fundamental importance to them in modern investigations about the search of universal roads to chaos. Among these applications, we have chosen the analysis of the main renormalization group techniques, which have the purpose of getting the quantitative microcharacterization of the transition from order to quantum chaos.