论文标题
奇异双曲线吸引子的稳健传递性
Robust transitivity of singular hyperbolic attractors
论文作者
论文摘要
奇异的双曲线是一种弱的双曲线形式，已针对矢量场引入，以便在非随身携带的集合中允许非分离的奇异性。洛伦兹吸引子是奇异双曲线集的一个典型例子。但是，与均匀的双曲线相反，奇异的双曲线并不意味着诸如传递性等强大的拓扑特性。 在本文中，我们证明了紧凑型歧管的$ c^1 $向量场的空间内，任何奇异的双曲线吸引子都是牢固地传递的。
Singular hyperbolicity is a weakened form of hyperbolicity that has been introduced for vector fields in order to allow non-isolated singularities inside the non-wandering set. A typical example of a singular hyperbolic set is the Lorenz attractor. However, in contrast to uniform hyperbolicity, singular hyperbolicity does not immediately imply robust topological properties, such as the transitivity. In this paper, we prove that open and densely inside the space of $C^1$ vector fields of a compact manifold, any singular hyperbolic attractors is robustly transitive.
