发表机构
Institute of Mathematics and Statistics, University of São Paulo（圣保罗大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用Michael连续选择定理，针对不连续广义双曲分裂的Banach空间动力学，建立了上同调方程的有界连续解，证明了广义双曲微分同胚在扰动下的半共轭性，并对一维Morse-Smale系统的无限乘积获得了无扩张性的完全结构稳定性。
AI 中文摘要
我们提出了一种基于Michael连续选择定理的新方法，用于处理可能具有不连续广义双曲分裂的Banach空间动力学的稳定性问题。该方法将轨道方向的均匀可解性估计转化为上同调方程的有界连续解。对于一致全局$C^1$范畴中的广义双曲微分同胚，在足够小的有界Lipschitz扰动下，它产生了两个方向的连续半共轭；但未断言满射性。对于一维Morse-Smale系统的无限乘积，我们构造了相容的正向和反向上同调解算子，并在没有扩张性的情况下获得了完全的结构稳定性。该结果适用于每个$l^p(Z)$（$1\leq p\leq\infty$），包括耦合坐标的扰动。这些乘积没有紧致全局吸引子，并且对于$p=\infty$，具有不可数多个双曲不动点。支撑一般半共轭定理的连续选择论证是针对广义双曲余循环发展的，产生了上同调方程的有界连续可解性。余循环分析还为有界连续向量场上的诱导算子提供了Lipschitz阴影性质。
英文摘要
We introduce a new method based on Michael's continuous selection theorem for stability of Banach-space dynamics with possibly discontinuous generalized-hyperbolic splittings. The method converts uniform orbitwise solvability estimates into bounded continuous solutions of cohomological equations. For generalized-hyperbolic diffeomorphisms in the uniform global $C^1$ category, it yields continuous semiconjugacies in both directions under sufficiently small bounded Lipschitz perturbations; surjectivity is not asserted. For an infinite product of one-dimensional Morse-Smale systems, we construct compatible forward and reverse cohomological solution operators and obtain full structural stability without expansivity. This result holds on every $l^p(Z)$, $1\leq p\leq\infty$, including perturbations that couple coordinates. These products have no compact global attractor and, for $p=\infty$, have uncountably many hyperbolic fixed points. The continuous-selection argument underlying the general semiconjugacy theorem is developed for generalized-hyperbolic cocycles, yielding bounded continuous solvability of cohomological equations. The cocycle analysis also gives Lipschitz shadowing for the induced operator on bounded continuous vector fields.
Comments48 pages
