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The aim of this article is to prove that for the graphene model like for amodel considered by the physicist Hou on a kagome lattice, there exists aformula which is similar to the one obtained by Chambers for the Harper model.As an application, we propose a semi-classical analysis of the spectrum of theHou butterfly near a flat band.

Chambers's formula for the graphene and the Hou model with kagome periodicity and applications