Density of nonzero exponent of contraction for pinching cocycles in Hom(S1)

Abstract

We consider pinching cocycles taking values in the space of homeomorphisms of the circle over an hyperbolic base. Using the invariance principle of Malicet, we prove that the cocycles having nonzero exponents of contraction are dense. In this paper, we generalize some common notions an results known of linear cocycles and cocycles of diffeomorphisms, to the nonlinear non-differentiable case.