Geodesic
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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@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/}
}
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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/