arXiv 0812.15402008-12math.DS

$C^1$部分双曲符号同胚的非均匀中心聚束和遍历性的泛属性

Nonuniform Center Bunching and the Genericity of Ergodicity among $C^1$ Partially Hyperbolic Symplectomorphisms

Artur Avila, Jairo Bochi, Amie Wilkinson

备注：: Final version. To appear in Annales Scientifiques de l'Ecole Normale Superieure
发表信息：: Annales Scientifiques de l'Ecole Normale Superieure, 42, n. 6 (2009), 931-979

摘要：

本文引入了部分双曲双同态的非均匀中心聚束的概念，推广了Burns-Wilkinson和Avila-Santamaria-Viana的结果。结合这一新技术与其他结构，我们证明了$C^1$ -一般部分双曲辛同胚遍历。我们还构造了新的例子稳定遍历部分双曲型同态。

英文摘要：

We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns--Wilkinson and Avila--Santamaria--Viana. Combining this new technique with other constructions, we prove that $C^1$-generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.

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