Expanding actions: minimality and ergodicity

Abstract

We prove that every expanding minimal semigroup action of $C^1$ diffeomorphisms of a compact manifold (resp. $C^{1+\alpha }$ conformal) is robustly minimal (resp. ergodic with respect to Lebesgue measure). We also show how, locally, a blending region yields the robustness of the minimality and implies ergodicity.

References in corpus (3)

• Symbolic blender-horseshoes and applications
• Robust minimality of iterated function systems with two generators
• Dynamics of iterated function systems on the circle close to rotations

Cited by in corpus (4)

• On the chaos game of Iterated Function Systems
• Stable local dynamics: expansion, quasi-conformality and ergodicity
• Minimal Strong Foliations in Skew-products of Iterated Function Systems
• Ergodicity of non-autonomous discrete systems with non-uniform expansion