Harmonicity of the Lyapunov exponent for monotonic cocycles and a generalized Thouless formula
Volume 269 / 2025
Fundamenta Mathematicae 269 (2025), 249-260
MSC: Primary 30Exx; Secondary 28Dxx, 37Dxx
DOI: 10.4064/fm288-4-2025
Published online: 15 June 2025
Abstract
In the case of Schrödinger cocycles, by the so-called Thouless formula the harmonicity of the Lyapunov exponent is equivalent to uniform hyperbolicity. In this paper we consider monotonic cocycles and give a sufficient condition for the harmonicity of the Lyapunov exponent to be equivalent to uniform hyperbolicity. We then generalize the Thouless formula to more general cocycles.
