AI 中文总结
研究巴拿赫空间和具有衰减性质的格中映射的退化不动点，将退化不动点不变流形存在性结果扩展到格系统，如在托达晶格扰动中找到此类流形。
AI 中文摘要
退化不动点出现在天体力学、经济学和化学等诸多有趣问题中。格系统，即由相互局部作用的无限阵列有限维子系统组成的动力系统，出现在生物学、物理学和数学的许多模型中。在这项工作中，我们将关于退化不动点稳定和不稳定不变流形存在性的结果扩展到具有衰减性质的格系统。例如，我们在托达晶格的扰动中找到了这样的流形。
英文摘要
Degenerate fixed points of maps appear in many interesting problems in Celestial Mechanics, Economics and Chemistry. Lattice systems, that is, dynamical systems consisting in an infinite array of finite dimensional subsystems interacting locally among them appear in many models of Biology, Physics and Mathematics. In this work, we extend the results concerning the existence of stable and unstable invariant manifolds of degenerate fixed points to lattice systems with decay properties. As an example, we find such manifolds in perturbations of the Toda lattice.
