Persistent nonhyperbolic transitive diffeomorphisms. (English) Zbl 0852.58066

Bonatti, Christian; Díaz, Lorenzo J.

Ann. Math. (2) 143, No. 2, 357-396 (1996).

The paper constructs a large class of \(C^1\)-persistent, nonhyperbolic, transitive diffeomorphisms of a closed manifold of dimension \(m \geq 3\) that carries a \(C^\infty\) transitive Anosov vector field. Some of them are isotopic to the identity. Others are partially hyperbolic diffeomorphisms with a central space of dimension greater than one. An essential element of the proofs is the use of so-called center-stable blenders, which are kinds of higher-dimensional horseshoes.

Reviewer: R.Schimming (Greifswald)

MSC:

37D99

Dynamical systems with hyperbolic behavior

Keywords:

nonhyperbolic diffeomorphisms; Anosov vector fields; attractors