Bowen因子的阶与单同态的内射编码
The degree of Bowen factors and injective codings of diffeomorphisms
摘要：
我们证明了O。Sarig曲面的超同态诱导了大集上的Hölder连续共轭。我们从它们的Bowen性质推导出这一点。这个概念，介绍了在一个联合工作与M。波义耳，概括了一个事实首先观察到的R。Bowen关于马尔可夫分割。我们依赖于有限等价理论和魔词同构中的度的概念。作为一个应用程序，我们给出了下界的周期点的数量第一表面的超同态（改进的结果Sarig）和西奈台球地图（建立在结果的Baladi和Demers）。最后，我们的特征表面的超同态承认一个Hölder连续编码的所有非周期双曲措施，并给出了一个稍弱的建设保持局部紧性。
英文摘要：
We show that symbolic finite-to-one extensions of the type constructed by O. Sarig for surface diffeomorphisms induce Hölder-continuous conjugacies on large sets. We deduce this from their Bowen property. This notion, introduced in a joint work with M. Boyle, generalizes a fact first observed by R.\ Bowen for Markov partitions. We rely on the notion of degree from finite equivalence theory and magic word isomorphisms. As an application, we give lower bounds on the number of periodic points first for surface diffeomorphisms (improving a result of Sarig) and for Sinai billiards maps (building on a result of Baladi and Demers). Finally we characterize surface diffeomorphisms admitting a Hölder-continuous coding of all their aperiodic hyperbolic measures and give a slightly weaker construction preserving local compactness.
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