Robust minimality of iterated function systems with two generators

TL;DR

This paper demonstrates that any compact manifold can have a pair of diffeomorphisms that generate minimal dynamics robustly in the $C^1$ topology, with applications to blenders and transitive skew products.

Contribution

It establishes the existence of robust minimal diffeomorphism pairs on any compact manifold, advancing the understanding of robust dynamical behaviors.

Findings

Existence of $C^1$ robustly minimal diffeomorphisms on all compact manifolds

Construction of blenders and robustly transitive skew products

Extension of minimal dynamics theory to broader classes of manifolds

Abstract

We prove that any compact manifold without boundary admits a pair of diffeomorphisms that generates $C^1$ robustly minimal dynamics. We apply the results to the construction of blenders and robustly transitive skew product diffeomorphisms.