The entropy spectrum of the center Lyapunov exponents for partially hyperbolic systems

In this paper, we study the entropy spectrum of the center Lyapunov exponents for a class of transitive partially hyperbolic diffeomorphisms with a one-dimensional center bundle. We show that if the strong unstable foliation is minimal, then the topological entropy of the level sets defined by the negative center Lyapunov exponents varies continuously with respect to the center Lyapunov exponents, and the variational principle holds for such level sets.