正常扩张层片的分层持续存在
Persistence of stratification of normally expanded laminations
摘要：
这份手稿补充了Hirsch-Pugh-Shub（HPS）理论关于常双曲层合的持久性和Robinson定理关于满足公理A和强横截条件（SA）的双同态的结构稳定性。我们推广这些结果通过引入一个几何对象：分层的叠层。这是一个分层，其地层是层状的。我们的主要定理意味着一些层的持续性，其层通常是膨胀的。动力学是流形的$C^r$ -自同态（可能不可逆）。持久性意味着对于动力学的任何$C^r$ -扰动，存在由扰动保持的紧密的$C^r$ -分层。这个定理在它的基本陈述（分层是由一个独特的层）给出了自同态的正常扩展层的持久性，推广了HPS理论。这个定理的另一个应用是作为层的具有正常扩张的边界或角的子流形的持久性。此外，我们注意到SA同构给出了一个典型的分层：其层是谱分解的基本片的稳定集的分层。我们的主要定理，然后意味着持久性的一些“正常SA”的叠层，这不是正常双曲。
英文摘要：
This manuscript complements the Hirsch-Pugh-Shub (HPS) theory on persistence of normally hyperbolic laminations and the theorem of Robinson on the structural stability of diffeomorphisms that satisfy Axiom A and the strong transversality condition (SA). We generalize these results by introducing a geometric object: the stratification of laminations. It is a stratification whose strata are laminations. Our main theorem implies the persistence of some stratifications whose strata are normally expanded. The dynamics is a $C^r$-endomorphism of a manifold (which is possibly not invertible). The persistence means that for any $C^r$-perturbation of the dynamics, there exists a close $C^r$-stratification preserved by the perturbation. This theorem in its elementary statement (the stratification is constituted by a unique stratum) gives the persistence of normally expanded laminations by endomorphisms, generalizing HPS theory. Another application of this theorem is the persistence, as stratifications, of submanifolds with boundary or corners normally expanded. Moreover, we remark that SA diffeomorphism gives a canonical stratifications: the stratification whose strata are the stable sets of basic pieces of the spectral decomposition. Our Main theorem then implies the persistence of some ``normally SA'' laminations which are not normally hyperbolic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
