English

Iteration of polynomial pair under Thue-Morse dynamic

Dynamical Systems 2014-03-11 v1

Abstract

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 {2cos2nx:n1}\{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.

Keywords

Cite

@article{arxiv.1403.2257,
  title  = {Iteration of polynomial pair under Thue-Morse dynamic},
  author = {Qinghui Liu and Yanhui Qu},
  journal= {arXiv preprint arXiv:1403.2257},
  year   = {2014}
}