论文标题
关于烟灰吸引子的混乱行为
On Chaotic Behavior of ASH Attractors
论文作者
论文摘要
渐近截面双曲线是一个弱的双曲线概念，可以正确地扩展截面的毛细血管，并将Rovella吸引子作为原型示例。该定义的主要特征是在奇异稳定歧管之外的点上存在任意较大的双曲线时间。在本文中，我们将证明，在满足这种超宽容性的三维流形上，与$ c^1 $ vector field $ x $相关的任何吸引子都是恢复表达的，并且对初始条件提出了敏感性。
The asymptotic sectional hyperbolicity is a weak notion of hyperbolicity that extends properly the sectional-hyperbolicity and includes the Rovella attractor as a archetypal example. The main feature of this definition is the existence of arbitrarily large hyperbolic times for points outside the stable manifolds of the singularities. In this paper we will prove that any attractor associated to a $C^1$ vector field $X$ on a three-dimensional manifold satisfying this kind of hyperbolicity is rescaling-expansive and presents sensitiveness respect to initial conditions.
