On the Lyapunov exponent and exponential dichotomy for the quasi-periodic Schrödinger operator
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 149-161
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Zbl MR
In this paper we study the Lyapunov exponent $\beta(E)$ for the one-dimensional Schrödinger operator with a quasi-periodic potential. Let $\Gamma\subset \mathbb{R}^{k}$ be the set of frequency vectors whose components are rationally independent. Let $\Gamma\subset \mathbb{R}^{k}$, and consider the complement in $\Gamma \times C^{r} (\mathbb{T}^{k} )$ of the set $\mathcal{D}$ where exponential dichotomy holds. We show that $\beta=0$ is generic in this complement. The methods and techniques used are based on the concepts of rotation number and exponential dichotomy.
Fabbri, R. On the Lyapunov exponent and exponential dichotomy for the quasi-periodic Schrödinger operator. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 149-161. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a6/
@article{BUMI_2002_8_5B_1_a6,
author = {Fabbri, R.},
title = {On the {Lyapunov} exponent and exponential dichotomy for the quasi-periodic {Schr\"odinger} operator},
journal = {Bollettino della Unione matematica italiana},
pages = {149--161},
year = {2002},
volume = {Ser. 8, 5B},
number = {1},
zbl = {1177.34108},
mrnumber = {MR1881929},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a6/}
}
TY - JOUR AU - Fabbri, R. TI - On the Lyapunov exponent and exponential dichotomy for the quasi-periodic Schrödinger operator JO - Bollettino della Unione matematica italiana PY - 2002 SP - 149 EP - 161 VL - 5B IS - 1 UR - http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a6/ LA - en ID - BUMI_2002_8_5B_1_a6 ER -