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arXiv · 1307.6054

Expanding actions: minimality and ergodicity

Pablo G. Barrientos·Abbas Fakhari·Dominique Malicet·Ali Sarizadeh
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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.

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Pablo G. Barrientos, Abbas Fakhari, Dominique Malicet, Ali Sarizadeh. 2013-07-23. Expanding actions: minimality and ergodicity. https://doi.org/10.1142/s0219493717500319

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