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 ωₙ=ω_n-1²-2, 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.
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Oliveira et al. (1984) studied this question.
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