论文标题
关于牢固及其奇异性的局部双曲线
On the partial hyperbolicity of robustly transitive sets with singularities
论文作者
论文摘要
同型线粒体的角度和奇异的双曲线与载体场的palis猜想有关。最近的作品对典型的三维矢量场进行了充分的理解。我们研究了远离同层次切线的较高维矢量场的动力学。更准确地说，我们证明，对于\ emph {any}尺寸矢量场，它远离同层次的切线，其稳健及时的奇异奇异集中包含的所有奇异性都是双曲线，并且具有相同的索引。此外，如果具有同质斜切的矢量不能累积矢量字段，则稳健的传递集为{$ c^1 $ - 基因}部分双曲线。
Homoclinic tangencies and singular hyperbolicity are involved in the Palis conjecture for vector fields. Typical three dimensional vector fields are well understood by recent works. We study the dynamics of higher dimensional vector fields that are away from homoclinic tangencies. More precisely, we prove that for \emph{any} dimensional vector field that is away from homoclinic tangencies, all singularities contained in its robustly transitive singular set are all hyperbolic and have the same index. Moreover, the robustly transitive set is {$C^1$-generically }partially hyperbolic if the vector field cannot be accumulated by ones with a homoclinic tangency.
