We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one-dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold. © 2009 Elsevier B.V. All rights reserved.
Saghin, R., & Xia, Z. (2010). The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center. Topology and Its Applications, 157(1), 29–34. https://doi.org/10.1016/j.topol.2009.04.053