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On the Lyapunov exponent and exponential dichotomy for the quasi-periodic Schrödinger operator

R. Fabbri — 2002

Bollettino dell'Unione Matematica Italiana

In this paper we study the Lyapunov exponent β E for the one-dimensional Schrödinger operator with a quasi-periodic potential. Let Γ R k be the set of frequency vectors whose components are rationally independent. Let Γ R k , and consider the complement in Γ C r T k of the set D where exponential dichotomy holds. We show that β = 0 is generic in this complement. The methods and techniques used are based on the concepts of rotation number and exponential dichotomy.

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