Bonatti, Christian; Díaz, Lorenzo J. Persistent nonhyperbolic transitive diffeomorphisms. (English) Zbl 0852.58066 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) Cited in 4 ReviewsCited in 71 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior Keywords:nonhyperbolic diffeomorphisms; Anosov vector fields; attractors PDF BibTeX XML Cite \textit{C. Bonatti} and \textit{L. J. Díaz}, Ann. Math. (2) 143, No. 2, 357--396 (1996; Zbl 0852.58066) Full Text: DOI OpenURL