Article
Preprint
On Positive Lyapunov exponent for the skew-shift potential
Helge Krüger
I will prove that for most energies E
and some frequencies \alpha
the Lyapunov exponent of the Schrödinger operator with
potential V(n) = 2 λ \cos(2\pi \alpha n2) has the
behavior L(E) \gtrsim λ2 as \lam → 0.
This improves upon earlier results by Bourgain.
MSC2000: Primary 81Q10; Secondary 37D25
Keywords: Lyapunov Exponents, Schrödinger Operators