We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense. To establish these results, we develop new perturbation tools for the $C^1$ topology: linearization of horseshoes while preserving entropy, and creation of "superblenders" from hyperbolic sets with large entropy.

中文翻译：

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C1 稳定遍历密度

我们证明了 Pugh 和 Shub 猜想的 $C^1$ 版本：在部分双曲体积保持 $C^r$ 微分同胚中，$r>1$，稳定遍历的 $C^1$-dense。为了建立这些结果，我们为 $C^1$ 拓扑开发了新的扰动工具：在保留熵的同时线性化马蹄铁，以及从具有大熵的双曲集创建“超级混合器”。