Mathematische Zeitschrift

, Volume 291, Issue 3–4, pp 931–958 | Cite as

Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles

  • Ao Cai
  • Claire Chavaudret
  • Jiangong You
  • Qi ZhouEmail author


We show that if the base frequency is Diophantine, then the Lyapunov exponent of a \(C^{k}\) quasi-periodic \(SL(2,{\mathbb {R}})\) cocycle is 1 / 2-Hölder continuous in the almost reducible regime. As a consequence, we show that if the frequency is Diophantine, and the potential is small, then the integrated density of states of the corresponding quasi-periodic Schrödinger operator is 1 / 2-Hölder continuous.



C. Chavaudret was supported by the ANR “BEKAM” and the ANR “Dynamics and CR Geometry”. J. You was partially supported by NSFC grant (11471155) and 973 projects of China (2014CB340701). Q. Zhou was partially supported by NSFC grant (11671192), “Deng Feng Scholar Program B” of Nanjing University, Specially-appointed professor programe of Jiangsu province.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ao Cai
    • 1
  • Claire Chavaudret
    • 2
  • Jiangong You
    • 3
  • Qi Zhou
    • 1
    Email author
  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Laboratoire J.A. DieudonnéUniversité de Nice-Sophia Antipolis (Parc Valrose)Nice Cedex 02France
  3. 3.Chern Institute of Mathematics and LPMCNankai UniversityTianjinChina

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