%0 Journal Article
%T Iteration of polynomial pair under Thue-Morse dynamic
%A Qinghui Liu
%A Yanhui Qu
%J Mathematics
%D 2014
%I arXiv
%X We study the behavior of a polynomial sequence which is defined by iterating a polynomial pair under Thue-Morse dynamic. We show that in suitable sense, the sequence will behave like $\{2\cos 2^nx: n\ge 1\}$. Basing on this property we can show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian has a common positive lower bound for all coupling.
%U http://arxiv.org/abs/1403.2257v1