Robustly transitive maps with critical points and large dimensional central spaces

Juan C. Morelli

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arXiv · 2510.10722

Robustly transitive maps with critical points and large dimensional central spaces

Juan C. Morelli

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Abstract

Given any triplet of positive integers $n \geq 2$, $m$ and $k$ such that $n=m+k$, we exhibit a $C^1$ robustly transitive endomorphism of $\mathbb{T}^n$ with persistent critical points in the isotopy class of $F \times Id$, where $F$ is an expanding map of $\mathbb{T}^m$ and $Id$ is the identity of $\mathbb{T}^k$. Furthermore, if $k$ is small, the map is not only in the isotopy class but in fact a perturbation of $F \times Id$.

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Juan C. Morelli. 2025-10-12. Robustly transitive maps with critical points and large dimensional central spaces. https://arxiv.org/abs/2510.10722

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