Uniform spectral properties of one-dimensional quasicrystals, II. The Lyapunov exponent

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dc.creatorDamanik, David
dc.creatorLenz, Daniel
dc.date1999-05-16
dc.date.accessioned2026-07-07T04:32:49Z
dc.date.available2026-07-07T04:32:49Z
dc.descriptionIn this paper we introduce a method that allows one to prove uniform local results for one-dimensional discrete Schrödinger 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.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math-ph/9905008
dc.identifierhttp://arxiv.org/abs/math-ph/9905008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58334
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject81Q10, 47B80
dc.titleUniform spectral properties of one-dimensional quasicrystals, II. The Lyapunov exponent
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