Robust transitivity for endomorphisms admitting critical points. (English) Zbl 1354.37036
Summary: We address the problem of giving necessary and sufficient conditions in order to have robustly transitive endomorphisms admitting persistent critical sets. We exhibit different types of open examples of robustly transitive maps in any isotopic class of endomorphisms acting on the two dimensional torus admitting persistent critical points. We also provide some necessary conditions for robust transitivity in this setting.
MSC:
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 37D30 | Partially hyperbolic systems and dominated splittings |
| 08A35 | Automorphisms and endomorphisms of algebraic structures |
References:
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