New proof of continuity of Lyapunov exponents for a class of smooth Schrödinger cocycles with weak Liouville frequencies

Abstract

We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a C2 cos-type potential and a weak Liouville frequency. We propose a new method to prove that the Lyapunov exponent is continuous in energies. In particular, a large deviation theorem is not needed in the proof.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11771205).

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Correspondence to Fan Wu.

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Fu, L., Xu, J. & Wu, F. New proof of continuity of Lyapunov exponents for a class of smooth Schrödinger cocycles with weak Liouville frequencies. Front. Math. China 15, 467–489 (2020). https://doi.org/10.1007/s11464-020-0843-z

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Keywords

  • Schrödinger cocycle
  • Lyapunov exponent (LE)
  • weak Liouville frequency
  • C2 cos-type potential
  • large deviation theorem (LDT)

MSC

  • 37A30