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Robust transitivity and domination for endomorphisms displaying critical points
Published online by Cambridge University Press: 14 April 2023
Abstract
We show that robustly transitive endomorphisms of a closed manifold must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive endomorphisms. To obtain the result, we must understand the structure of the kernel of the differential and the recurrence to the critical set of the endomorphism after perturbation.
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- © The Author(s), 2023. Published by Cambridge University Press