论文标题
部分可观测时空混沌系统的无模型预测
$C^r$-Chain closing lemma for certain partially hyperbolic diffeomorphisms
论文作者
论文摘要
对于\ mathbb {n} _ {\ geq 2} \ cup \ {\ infty \} $的每一个$ r \，我们证明了一个$ c^r $ -Orbit，将Lemma连接起来，用于动态相干和斑块的宽敞和斑块膨胀的部分超质型二型伪造，并具有1-二维的1-二级固定确定性确定性的中心。确切地说，对于这种差异性$ f $，如果$ y $是可以从$ x $到pseudo-orbits获得的链条，那么对于任何附近的$ u $ $ x $ us $ x $和任何$ y $ y $的邻居$ v $ $ y $，就存在$ u $从$ u $到$ v $ by nutally $ c^r $ c^r $ -small-small-small-small perttertations。结果，我们证明，对于此类中的$ c^r $形式的差异性，周期点在链条复发集中是密集的，链条传递性意味着传递性。
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 1-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.
