On the Lyapunov Exponents for a Class of Circle Diffeomorphisms Driven by Expanding Circle Endomorphisms

Abstract

We consider skew-product maps on mathbb {T}^2 of the form F(x,y)=(bx,x+g(y)) where g:mathbb {T}rightarrow mathbb {T} is an orientation-preserving C^2-diffeomorphism and bge 2 is an integer. We show that the fibred (upper and lower) Lyapunov exponent of almost every point (x, y) is as close to int _mathbb {T}log (g'(eta ))deta as we like, provided that b is large enough.