On characterization of the onset to chaos

The purpose of this paper is to introduce the family of Metallic Means, whose members are the well known Golden Mean and its relatives, the Silver Mean, Bronze Mean, Copper Mean, Nickel Mean, etc. Bringing out, from the mathematical point of view, their similarities as well as their differences, it is possible to find a universal behavior on the roads to chaos, a major problem which is still open for further research.