2021/06/07 by Cristina Lizana, Rafaël Potrie, Lizana, C. +5 · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2106.03291
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.