论文标题
对渐近分节双曲线流的理论的贡献
Contributions to the Theory of Asymptotically Sectional Hyperbolic Flows
论文作者
论文摘要
在本文中，我们为渐近的截面 - 纤维化（ASH）流的理论做出了一些贡献。首先，我们证明每个$ c^2 $ vector场上的恒星灰吸引子实际上都是截面hyperbolic（SH）。其次，我们确定所有灰烬吸引者都表现出熵柔韧性的特性。此外，我们表明，三维矢量场的任何灰分吸引子都是熵的，并且可以定期轨道。最后，我们为烟灰吸引子中周期轨道的生长速率提供了下限。
In this paper, we make several contributions to the theory of asymptotically sectional-hyperbolic (ASH) flows. First, we prove that every star ASH attractor for a $C^2$ vector field is, in fact, sectional-hyperbolic (SH). Second, we establish that all ASH attractors exhibit the property of entropy flexibility. Additionally, we show that any ASH attractor for three-dimensional vector fields is entropy-expansive and admits periodic orbits. Finally, we provide a lower bound for the growth rate of periodic orbits in an ASH attractor.
