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Almost Everywhere Positivity of the Lyapunov Exponent for the Doubling Map

Damanik, David and Killip, Rowan (2005) Almost Everywhere Positivity of the Lyapunov Exponent for the Doubling Map. Communications in Mathematical Physics, 257 (2). pp. 287-290. ISSN 0010-3616. doi:10.1007/s00220-004-1261-x.

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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.

Item Type:Article
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URLURL TypeDescription Paper ReadCube access
Damanik, David0000-0001-5924-3849
Killip, Rowan0000-0002-4272-7916
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.
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Issue or Number:2
Record Number:CaltechAUTHORS:20170408-161314581
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Official Citation:Damanik, D. & Killip, R. Commun. Math. Phys. (2005) 257: 287. doi:10.1007/s00220-004-1261-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76149
Deposited By: 1Science Import
Deposited On:10 Jul 2017 18:46
Last Modified:15 Nov 2021 16:57

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