Gene

Quantum mechanics

Linguistics

Chaotic

Hölder condition

Philosophy

Pure mathematics

Diophantine approximation

Exponent

Astrophysics

Biochemistry

Computer science

Physics

Nonlinear system

Mathematics

Lyapunov exponent

Quasi periodic

Differentiable function

Transcription factor

Mathematical analysis

Artificial intelligence

Diophantine equation

Repressor

Chemistry

Operator (biology)

Mathematische Zeitschrift

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.

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