## Persistent nonhyperbolic transitive diffeomorphisms.(English)Zbl 0852.58066

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.

### MSC:

 37D99 Dynamical systems with hyperbolic behavior
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