Discontinuity of the Lyapunov Exponent

Abstract

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.

References in corpus (2)

• Probabilistic averages of Jacobi operators
• An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups

Cited by in corpus (2)

• On the spectrum of skew-shift Schrödinger operators
• Some Spectrum Property of Periodic Coupling AMO Operator