Continuity of Lyapunov Exponent for Quasi-Periodic Gevrey Cocycles

TL;DR

This paper proves the continuity of the Lyapunov exponent for certain quasi-periodic cocycles in Gevrey spaces with specific frequency conditions, expanding understanding of stability in dynamical systems.

Contribution

It establishes the continuity of the Lyapunov exponent for Gevrey cocycles under subexponential Brjuno frequency conditions, a novel result in the field.

Findings

Lyapunov exponent is continuous for $1<s+ta<2$ in Gevrey cocycles.

Continuity holds under subexponential Brjuno class frequency.

Results extend stability analysis in quasi-periodic dynamical systems.

Abstract

It is shown that for the quasi-periodic cocycles in Gevrey space $G^{s}$ and subexponential Brjuno class frequency $\Omega(\eta)$, the Lyapunov exponent is continuous provided that $1<s+\eta<2$.