Discontinuity of the Lyapunov Exponent
Spectral Theory
2015-03-17 v1 Mathematical Physics
math.MP
Abstract
We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schr\"odinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose Lyapunov exponent is discontinuous, are dense in the space of limit-periodic potentials.
Keywords
Cite
@article{arxiv.1005.0181,
title = {Discontinuity of the Lyapunov Exponent},
author = {Zheng Gan and Helge Krueger},
journal= {arXiv preprint arXiv:1005.0181},
year = {2015}
}