Article
Preprint
Discontinuity of the Lyapunov exponent
Zheng Gan and Helge Krüger
We study discontinuity of the Lyapunov exponent. We construct a
limit-periodic Schrödinger 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.
MSC2000: 34D08; 39A70, 47A10
Keywords: Schrödinger operator, Lyapunov exponent, limit-periodic potential