Abstract

This paper presents a brief survey for the theory of stability of weakly hyperbolic invariant sets. It has been proved in several papers that I published along with Pliss and Sell that a weakly hyperbolic invariant set is stable even if the Lipschitz condition fails to hold. However, the uniqueness of leaves of a weakly hyperbolic invariant set of a perturbed system remains an open question. We show that this problem is connected to the so-called plaque expansivity conjecture in the theory of dynamical systems.

中文翻译：

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弱双曲不变集的稳定性理论问题

摘要

本文简要介绍了弱双曲不变集的稳定性理论。我与Pliss和Sell共同发表的几篇论文证明，即使Lipschitz条件无法成立，弱双曲不变集也是稳定的。然而，微分双曲不变系统的叶子的唯一性仍然是一个悬而未决的问题。我们证明了这个问题与动力系统理论中所谓的斑块膨胀性猜想有关。