Uniform positivity of the Lyapunov exponent for monotone potentials generated by the doubling map

Abstract

We show that for any doubling map generated $C^1$ monotone potential with derivative uniformly bounded away from zero, the Lyapunov exponent of the associated Schrödinger operators is uniformly positive for all energies provided the coupling constant is large.

13 pages

References in corpus (1)

• Positive Lyapunov Exponents for Quasiperiodic Szego cocycles

Cited by in corpus (1)

• Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent