论文标题
关于奇异统治和（多）奇异超质性的概念
On the notions of singular domination and (multi-)singular hyperbolicity
论文作者
论文摘要
引入了统一双曲线和主导分裂的特性，以研究差异性动力学的稳定性。当人们试图将这些定义扩展到向量场时，人们会遇到困难，而Shantao Liao表明，考虑线性庞加莱流而不是切线流以研究衍生物的性质更为相关。在本文中，我们定义了奇异统治的概念，这是线性庞加莱流的主导分裂的类似物，在扰动下是可靠的。基于此，我们给出了多单明一重的双曲线的新定义，这相当于Bonatti-da Luz最近引入的多余性。我们定义的新颖性是，它不涉及奇异集的爆炸和线性流的重新归一化合作。
The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms. One meets difficulties when one tries to extend these definitions to vector fields and Shantao Liao has shown that it is more relevant to consider the linear Poincaré flow rather than the tangent flow in order to study the properties of the derivative. In this paper we define the notion of singular domination, an analog of the dominated splitting for the linear Poincaré flow which is robust under perturbations. Based on this, we give a new definition of multi-singular hyperbolicity which is equivalent to the one recently introduced by Bonatti-da Luz. The novelty of our definition is that it does not involve the blowup of the singular set and the renormalization cocycle of the linear flows.
