ABSTRACT
An electric current does not have a secret reverse side; it is nothing but the totality of the physical–chemical actions which manifest it (electrolysis, the incandescence of a carbon filament, the displacement of the needle of a galvanometer, etc.). Two elements are essential to an attracting set: first the attracting set is a closed invariant set; second, there has to be something that is attracted: the readers expect at least orbits starting nearby the attracting set to be attracted to it. In cases like the Duffing oscillator, the Lorenz system and the forced CO2 laser, in which the readers find more than one attractor, there exists an invariant set that includes those points in phase space that are in the limit between the two basins of attraction. This chapter concludes that the saddle is necessarily in the common boundary between the two basins of attraction and is the limit point for orbits belonging to the boundary.
