部分双曲同态与Lagrange切触结构
Partially hyperbolic diffeomorphisms and Lagrangian contact structures
摘要：
本文对稳定分布、不稳定分布和中心分布光滑且非徘徊集等于整个流形的三维切触部分双曲同态进行了分类。我们证明，在有限商或有限幂的情况下，它们光滑地共轭于代数接触-Anosov流的时间一映射，或零流形的仿射部分双曲自同构。由这三个不变分布引起的刚性几何结构在证明中起着基础性的作用。
英文摘要：
In this paper, we classify the three-dimensional contact partially hyperbolic diffeomorphisms whose stable, unstable and central distributions are smooth, and whose non-wandering set equals the whole manifold. We prove that up to a finite quotient or a finite power, they are smoothly conjugated either to the time-one map of an algebraic contact-Anosov flow, or to an affine partially hyperbolic automorphism of a nil-manifold. The rigid geometric structure induced by the three invariant distributions plays a fundamental role in the proof.
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