Smooth zero-entropy diffeomorphisms with ergodic derivative extension

Abstract

On any smooth compact and connected manifold of dimension 2 admitting a smooth non-trivial circle action we construct $C^{\infty }$-diffeomorphisms of topological entropy zero whose differential is ergodic with respect to a smooth measure in the projectivization of the tangent bundle. The proof is based on a version of the “approximation-by-conjugation”-method.