Partial hyperbolicity and specification
Partial hyperbolicity and specification
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DOI：
10.1090/proc/12830
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发表时间：
2013-07
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通讯作者：
Naoya Sumi;P. Varandas;Kenichiro Yamamoto
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作者：
Naoya Sumi;P. Varandas;Kenichiro Yamamoto
研究了部分双曲型动力系统的规范性质。特别地，我们证明了如果一个部分双曲同态有两个不同指标的鞍，并且其中一个鞍的稳定流形与强稳定叶重合，则它不满足规范化性质.作为应用，我们证明了在三维闭流形上的鲁棒非双曲传递同态集合中存在C1-开稠密子集P，使得P中的非双曲同态不满足规范性质.
We study the specification property for partially hyperbolic dy- namical systems. In particular, we show that if a partially hyperbolic diffeo- morphism has two saddles with different indices, and stable manifold of one of them coincides with the strongly stable leaf, then it does not satisfy the spec- ification property. As an application, we prove that there exists a C 1 -open and dense subset P in the set of robustly non-hyperbolic transitive diffeomor- phisms on a three dimensional closed manifold such that diffeomorphisms in P do not satisfy the specification property.