Communications in Mathematical Physics

, Volume 267, Issue 3, pp 735–740 | Cite as

Cantor Spectrum and KDS Eigenstates

  • Joaquim PuigEmail author


In this note we consider KDS eigenstates of one-dimensional Schrödinger operators with ergodic potential, which are a class of generalized eigenfunctions including Bloch eigenstates. We show that if the spectrum, restricted to an interval, has zero Lyapunov exponents and is a Cantor set, then for a residual subset of energies, KDS eigenstates do not exist. In particular, we show that the quasi-periodic Schrödinger operators whose Schrödinger quasi-periodic cocycles are reducible for all energies have a limit band-type spectrum.


Lyapunov Exponent Exponential Dichotomy Bloch Wave Positive Lyapunov Exponent Generalize Eigenfunctions 
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© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Departament de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain

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