一类一般鲁棒动力学的类混合性质
Mixing-like properties for some generic and robust dynamics
摘要：
我们证明了一个孤立的拓扑混合同宿类的一般同同态的Bernoulli测度集是一类支持的不变测度集的稠密子集。为此，我们引入了大周期属性，并表明这是这些类的一个强大的属性。我们还表明，整个流形是一个同宿类的一个开放的和稠密的子集集的鲁棒传递的同胚同胚远离同宿切线。特别地，利用Abdenur和Crockier的结果，我们得到了这个子集中的每个双同态都是鲁棒拓扑混合的。
英文摘要：
We show that the set of Bernoulli measures of an isolated topologically mixing homoclinic class of a generic diffeomorphism is a dense subset of the set of invariant measures supported on the class. For this, we introduce the large periods property and show that this is a robust property for these classes. We also show that the whole manifold is a homoclinic class for an open and dense subset of the set of robustly transitive diffeomorphisms far away from homoclinic tangencies. In particular, using results from Abdenur and Crovisier, we obtain that every diffeomorphism in this subset is robustly topologically mixing.
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