Chaotic renormalization approach to electronic systems

We have proved the equivalence between the density of electronic states of a linear tight-binding chain and the density of chaotic visits along the energy axis for the map ${\omega }_n={\omega }_{n-1\mathrm{}}^2-2\mathrm{}$, using a renormalization-group approach. Our results are generalized for other systems and for higher dimensions, providing a new, simple method for computing the density of states of any translationally invariant system with a known dispersion relation.