层压的持久性

摘要：

我们提出了一个现代的证明，一些著名的赫希-Pugh-舒布定理的持久性正常双曲紧层的扩展。我们的扩展包括允许的动力学是一个自同态，考虑复杂的分析情况下，并允许层压非紧。为了研究分析情况，我们使用复结构的变形形式。我们提出了出现在多个复变数动力学中的各种持久复叠层：Henon映射、纤维全纯映射.为了证明持久性定理，我们构造了一个关于稳定和不稳定的常双曲型层合的层合结构。

英文摘要：

We present a modern proof of some extensions of the celebrated Hirsch-Pugh-Shub theorem on persistence of normally hyperbolic compact laminations. Our extensions consist of allowing the dynamics to be an endomorphism, of considering the complex analytic case and of allowing the laminations to be non compact. To study the analytic case, we use the formalism of deformations of complex structures. We present various persistent complex laminations which appear in dynamics of several complex variables: Henon maps, fibered holomorphic maps... In order to proof the persistence theorems, we construct a laminar structure on the stable and unstable of the normally hyperbolic laminations.

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