Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum

Yoram Last*, Barry Simon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We provide a new proof of the theorem of Simon and Zhu that in the region E<λfor a.e. energies, -(d2/dx2)+λcos(xα), 0<α<1 has Lyapunov behavior with a quasi-classical formula for the Lyapunov exponent. We also prove Lyapunov behavior for a.e.E∈[-2,2] for the discrete model withV(j2)=ej,V(n)=0 ifn∉{1,4,9,...}. The arguments depend on a direct analysis of the equations for the norm of a solution.

Original languageEnglish
Pages (from-to)513-530
Number of pages18
JournalJournal of Functional Analysis
Volume154
Issue number2
DOIs
StatePublished - 20 Apr 1998
Externally publishedYes

Bibliographical note

Funding Information:
* This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The U.S. Government has certain rights in this material.

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