- 99-184 David Damanik, Daniel Lenz
- Uniform spectral properties of one-dimensional quasicrystals,
II. The Lyapunov exponent
(35K, LaTeX)
May 18, 99
-
Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers
-
Abstract. In this paper we introduce a method that allows one to prove uniform
local results for one-dimensional discrete Schr\"odinger operators with
Sturmian potentials. We apply this method to the transfer matrices in
order to study the Lyapunov exponent and the growth rate of
eigenfunctions. This gives uniform vanishing of the Lyapunov exponent
on the spectrum for all irrational rotation numbers. For irrational
rotation numbers with bounded continued fraction expansion, it gives
uniform existence of the Lyapunov exponent on the whole complex plane.
Moreover, it yields uniform polynomial upper bounds on the growth rate
of transfer matrices for irrational rotation numbers with bounded
density. In particular, all our results apply to the Fibonacci case.
- Files:
99-184.src(
99-184.comments ,
99-184.keywords ,
uniform2.tex )