Central Lyapunov exponent of partially hyperbolic diffeomorphisms of 𝕋³

Source abstract

In this paper we construct some “pathological” volume preserving partially hyperbolic diffeomorphisms on T 3 \mathbb T^{3} such that their behavior in small scales in the central direction (Lyapunov exponent) is opposite to the behavior of their linearization. These examples are isotopic to Anosov. We also get partially hyperbolic diffeomorphisms isotopic to Anosov (consequently with non-compact central leaves) with zero central Lyapunov exponent at almost every point.