For every $r\in \mathbb {N}_{\geq 2}\cup \{\infty \}$ , we prove a $C^r$ -orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with one-dimensional orientation preserving center bundle. To be precise, for such a diffeomorphism f, if a point y is chain attainable from x through pseudo-orbits, then for any neighborhood U of x and any neighborhood V of y, there exist true orbits from U to V by arbitrarily $C^r$ -small perturbations. As a consequence, we prove that for $C^r$ -generic diffeomorphisms in this class, periodic points are dense in the chain recurrent set, and chain transitivity implies transitivity.

中文翻译：

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-某些部分双曲微分同胚的链闭引理

对于每一个 $r\in \mathbb {N}_{\geq 2}\cup \{\infty \}$ ，我们证明一个 $C^r$ -轨道连接引理，用于具有一维方向保持中心束的动态相干和斑块扩展部分双曲微分同胚。准确地说，对于这样的微分同胚F，如果一个点y链可以从X通过伪轨道，然后对于任何邻域U的X和任何邻里V的y，存在真实轨道U到V任意地 $C^r$ - 小扰动。因此，我们证明对于 $C^r$ - 此类中的一般微分同胚，周期点在链循环集中密集，并且链传递性意味着传递性。