Journal
DUKE MATHEMATICAL JOURNAL
Volume 166, Issue 14, Pages 2697-2718Publisher
DUKE UNIV PRESS
DOI: 10.1215/00127094-2017-0013
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Funding
- European Research Council (ERC) Starting Grant Quasiperiodic
- Balzan project of Jacob Palis
- National Natural Science Foundation (NNSF) of China [11471155]
- National Basic Research Program (973 Program of China) [2014CB340701]
- Fondation Science Mathematiques de Paris
- ERC Starting Grant Quasiperiodic
- NNSF of China [11671192]
- Deng Feng Scholar Program B of Nanjing University
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It is known that the spectral type of the almost Mathieu operator (AMO) depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency. We study the competition between those factors and locate the point where the phase transition from singular continuous spectrum to pure point spectrum takes place, which solves Jitomirskaya's conjecture. Together with a previous work by Avila, this gives the sharp description of phase transitions for the AMO for the a.e. phase.
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