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

Yoram Last; Barry Simon

doi:10.1006/jfan.1997.3192

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 journal › Article › peer-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(x^α), 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)=e^j,V(n)=0 ifn∉{1,4,9,...}. The arguments depend on a direct analysis of the equations for the norm of a solution.

Original language	English
Pages (from-to)	513-530
Number of pages	18
Journal	Journal of Functional Analysis
Volume	154
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1997.3192
State	Published - 20 Apr 1998
Externally published	Yes

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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10.1006/jfan.1997.3192

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title = "Modified Pr{\"u}fer and EFGP Transforms and Deterministic Models with Dense Point Spectrum",

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.",

author = "Yoram Last and Barry Simon",

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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AU - Simon, Barry

N1 - 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.

PY - 1998/4/20

Y1 - 1998/4/20

N2 - 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.

AB - 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.

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

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