Uniform spectral properties of one-dimensional quasicrystals, iv. quasi-sturmian potentials
نویسندگان
چکیده
منابع مشابه
Uniform Spectral Properties of One-dimensional Quasicrystals, Iv. Quasi-sturmian Potentials
We consider discrete one-dimensional Schrr odinger operators with quasi-Sturmian potentials. We present a new approach to the trace map dy-namical system which is independent of the initial conditions and establish a characterization of the spectrum in terms of bounded trace map orbits. Using this, it is shown that the operators have purely singular continuous spectrum and their spectrum is a C...
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In 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 i...
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We apply the Jitomirskaya-Last extension of the Gilbert-Pearson theory to discrete one-dimensional Schrr odinger operators with potentials arising from generalized Fibonacci sequences. We prove for certain rotation numbers that for every value of the coup ling constant, there exists an > 0 such that the corresponding operator has purely-continuous spectrum. This result follows from uniform uppe...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2003
ISSN: 0021-7670,1565-8538
DOI: 10.1007/bf02786553