Connectedness of the set of central Lyapunov exponents

We show that there is a residual subset $\mathcal{R}$ of $Diff^1(M)$ 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.Comment: 12 pages, 3 figure