Abstract
When the binding energy of a two-body system goes to zero the two-body system
shows a continuous scaling invariance governed by the large value of the
scattering length. In the case of three identical bosons, the three-body system
in the same limit shows the Efimov effect and the scale invariance is broken to
a discrete scale invariance. As the number of bosons increases correlations
appear between the binding energy of the few- and many-body systems. We discuss
some of them as the relation between the saturation properties of the infinite
system and the low-energy properties of the few-boson system.