Abstract

The entropy conjecture states that for a $C1$ map on a compact manifold the topological entropy is greater or equal to the logarithm of the spectral radius of the map induced on the homology. It is proven in some cases (if the map is $C\infty$ or hyperbolic or the manifold is a torus or more general an infranil manifold) but still open for the general case. We will explain how to prove it for partially hyperbolic maps with one-dimensional center bundle. This is joint work with Jeff Xia.