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

Last, Yoram and Simon, Barry (1998) Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum. Journal of Functional Analysis, 154 (2). pp. 513-530. ISSN 0022-1236. https://resolver.caltech.edu/CaltechAUTHORS:20170906-104652888

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Abstract

We provide a new proof of the theorem of Simon and Zhu that in the region |E|<λ for a.e. energies, −(d^2/dx^2)+λ cos(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 with V(j^2)=e^j,V(n)=0 if n∉ {1, 4, 9,…}. The arguments depend on a direct analysis of the equations for the norm of a solution.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/jfan.1997.3192DOIArticle
http://www.sciencedirect.com/science/article/pii/S002212369793192XPublisherArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 1998 Academic Press. Received 13 June 1997, Accepted 20 August 1997. 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.
Funders:
Funding AgencyGrant Number
NSFDMS-9401491
Issue or Number:2
Record Number:CaltechAUTHORS:20170906-104652888
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170906-104652888
Official Citation:Yoram Last, Barry Simon, Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum, Journal of Functional Analysis, Volume 154, Issue 2, 1998, Pages 513-530, ISSN 0022-1236, http://dx.doi.org/10.1006/jfan.1997.3192. (http://www.sciencedirect.com/science/article/pii/S002212369793192X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81186
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:06 Sep 2017 18:09
Last Modified:03 Oct 2019 18:39

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