We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of Td with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on H1 (Td) is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example.
- derived from Anosov
- measures of maximal entropy
- partial hyperbolicity
- robustly transitive diffeomorphisms