论文标题
部分双曲线差异和拉格朗日接触结构
Partially hyperbolic diffeomorphisms and Lagrangian contact structures
论文作者
论文摘要
在本文中，我们对三维触点进行了分类，部分双曲线差异性稳定，不稳定和中央分布是光滑的，并且其非随身携带的集合等于整个歧管。我们证明，根据有限的商或有限的功率，它们可以平稳地与代数接触式流动的时间映射，或者与nil-manifold的部分双曲线自动形态相结合。由三个不变分布引起的刚性几何结构在证明中起着基本作用。
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.
