High dimensional robustly singular maps that are $C^1$ robustly transitive

TL;DR

This paper presents a new construction that encompasses all known examples of high-dimensional, $C^1$ robustly transitive maps with singularities, providing a sufficient condition for their existence on various compact manifolds.

Contribution

It introduces a unified construction and a sufficient condition for robust transitivity with singularities, advancing understanding of such maps on compact manifolds.

Findings

Unified construction includes all known examples

Provides a sufficient condition for robust transitivity with singularities

Applicable to a large class of compact manifolds

Abstract

We improve previous results by exhibiting a construction that contains all known examples. A suficient condition for the existence of robustly transitive maps displaying singularities on a certain large class of compact manifolds is given.