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. doi:10.1006/jfan.1997.3192. 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 | |||||||||
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| 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. | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1006/jfan.1997.3192 | |||||||||
| 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: | 15 Nov 2021 19:41 |
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