Published July 2005
| Submitted
Journal Article
Open
Almost Everywhere Positivity of the Lyapunov Exponent for the Doubling Map
- Creators
- Damanik, David
- Killip, Rowan
Abstract
We show that discrete one-dimensional Schrödinger operators on the half-line with ergodic potentials generated by the doubling map on the circle, V_θ(n)=f(2^nθ), may be realized as the half-line restrictions of a non-deterministic family of whole-line operators. As a consequence, the Lyapunov exponent is almost everywhere positive and the absolutely continuous spectrum is almost surely empty.
Additional Information
© Springer-Verlag Berlin Heidelberg 2005. Received: 14 April 2004 / Accepted: 1 June 2004 / Published online: 13 January 2005 Communicated by B. Simon. D. D. was supported in part by NSF grant DMS–0227289. We thank Svetlana Jitomirskaya and Barry Simon for useful conversations.Attached Files
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Additional details
- Eprint ID
- 76149
- DOI
- 10.1007/s00220-004-1261-x
- Resolver ID
- CaltechAUTHORS:20170408-161314581
- DMS–0227289
- NSF
- Created
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2017-07-10Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field