Walk inside Hofstadter's butterfly

J.P. Guillement , B. Helffer , P. Treton

This paper describes with help of numerically computed pictures the fascinating properties of the spectrum of Harper's equation in the spirit of celebrated Hofstadter's picture. We hope to explain recent results obtained by mathematicians and physicists about the Cantor structure of this spectrum.

Mots clés: difference equations

Domaines: Articles anciens

J.P. Guillement, B. Helffer, P. Treton. Walk inside Hofstadter's butterfly. Journal de Physique, 1989, 50 (15), pp.2019-2058. ⟨10.1051/jphys:0198900500150201900⟩. ⟨jpa-00211045⟩