Connectedness of the set of central Lyapunov exponents

Abstract

We show that there is a residual subset $\mathcal{R}$ of $Dif{f}^1(M)$ such that for any $f\in \mathcal{R}$ and any partially hyperbolic homoclinic class $H(p,f)$ with one dimensional center direction, the set of central Lyapunov exponents associated with the ergodic with either full support or positive entropy is an interval.

arXiv comment12 pages, 3 figures