Published May 2006
| Published
Journal Article
Open
Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials
- Creators
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Damanik, David
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Lenz, Daniel
Chicago
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Abstract
We consider discrete one-dimensional Schrödinger operators whose potentials belong to minimal subshifts of low combinatorial complexity and prove for a large class of such operators that the spectrum is a Cantor set of zero Lebesgue measure. This is obtained through an analysis of the frequencies of the subwords occurring in the potential. Our results cover most circle map and Arnoux–Rauzy potentials.
Additional Information
© 2005 Elsevier. Received 20 June 2005, Available online 13 December 2005. Supported in part by NSF grant DMS-0227289. We thank Artur Avila and Barry Simon for useful discussions. A substantial part of this work was done while one of the authors (D.L.) was visiting Caltech in September 2003. He would like to thank Barry Simon and the Department of Mathematics for the warm hospitality.Attached Files
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Additional details
- Eprint ID
- 76430
- Resolver ID
- CaltechAUTHORS:20170409-071347082
- NSF
- DMS-0227289
- Created
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2018-04-03Created from EPrint's datestamp field
- Updated
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2023-09-28Created from EPrint's last_modified field