We present an example of a $\mathcal{C}^1$-robustly transitive skew-product with non-trivial, non-hyperbolic action on homology. The example is conservative, ergodic, non-uniformly hyperbolic and its fiber directions cannot be decomposed into two dominated subbundles.

中文翻译：

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鲁棒传递微分同胚的一个新例子

我们提出了一个 $\mathcal{C}^1$-robustly 传递偏斜积的例子，它对同源具有非平凡的、非双曲的作用。该示例是保守的、遍历的、非均匀双曲线的，其纤维方向不能分解为两个主导子束。