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Original Article

Anosov–Katok Constructions for Quasi-Periodic SL(2,R) Cocycles

Université de Lille, Lille, France
Department of Mathematics, Nanjing University, Nanjing 210093, China
Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
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Abstract

We prove that if the frequency of the quasi-periodic SL(2,R) cocycle is Diophantine, then each of the following properties is dense in the subcritical regime: for any 12<κ<1, the Lyapunov exponent is exactly κ-Hölder continuous; the extended eigenstates of the potential have optimal sub-linear growth; and the dual operator associated with a subcritical potential has power-law decaying eigenfunctions. The proof is based on fibered Anosov–Katok constructions for quasi-periodic SL(2,R) cocycles.

Keywords

Quasi-periodicAnosov–Katok constructionAlmost-reducibility
Peking Mathematical Journal
Volume 7 Issue 1,
March 2024
Pages 203-245
DOI: 10.1007/s42543-022-00056-y
Cite this article:
Karaliolios, N., Xu, X. & Zhou, Q. Anosov–Katok Constructions for Quasi-Periodic SL(2,R) Cocycles. Peking Math J 7, 203-245 (2024). https://doi.org/10.1007/s42543-022-00056-y

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Received: 15 November 2021
Revised: 12 September 2022
Accepted: 05 October 2022
Published: 21 December 2022
© Peking University 2022
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