Robust transitivity and domination for endomorphisms displaying critical points
Dynamical Systems
2023-02-27 v4
Abstract
We show that robustly transitive endomorphisms of a closed manifolds 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.
Cite
@article{arxiv.2106.03291,
title = {Robust transitivity and domination for endomorphisms displaying critical points},
author = {C. Lizana and R. Potrie and E. R. Pujals and W. Ranter},
journal= {arXiv preprint arXiv:2106.03291},
year = {2023}
}
Comments
We rewrote Lemmas 2.7 and 4.7 in order to be clearer and add some referee's sugentions. We would like to thanks the referee for their suggestion and comments