"Mixed spectral nature" of Thue--Morse Hamiltonian

Qinghui Liu, Yanhui Qu, Xiao Yao

We find three dense subsets ${\Sigma }_I,{\Sigma }_{II}$ and ${\Sigma }_{III}$ of the spectrum of the Thue-Morse Hamiltonian, such that each energy in ${\Sigma }_I$ is extended, each energy in ${\Sigma }_{II}$ is pseudo-…