论文标题
关于Lipschitz操作员的动态
On the dynamics of Lipschitz operators
论文作者
论文摘要
通过不含Lipschitz的空间的线性化属性，任何Lipschitz地图$ f：m \ to n $之间的两个指数度量空间之间的n $可以独特地扩展到有界的线性操作员$ \ wideHat {f}：\ Mathcal f（mathcal f（m）\ to \ nathcal f（mathcal f ot \ nathcal f（n）之间，他们对应的LipsChitz-firepchitz-firee Spaces之间。在本说明中，我们探讨了Lipschitz自动映射的动力学之间的连接$ f：m \至m $与它们的扩展的线性动力学$ \ wideHat {f}：\ Mathcal f（m）\ to \ Mathcal f（mathcal f（mathcal f（m）$）。这不仅使我们能够将拓扑动力系统与线性动力学系统联系起来，而且还提供了一类新的高环，作用于Lipschitz的空间。
By the linearization property of Lipschitz-free spaces, any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended uniquely to a bounded linear operator $\widehat{f} : \mathcal F(M) \to \mathcal F(N)$ between their corresponding Lipschitz-free spaces. In this note, we explore the connections between the dynamics of Lipschitz self-maps $f : M \to M$ and the linear dynamics of their extensions $\widehat{f} : \mathcal F(M) \to \mathcal F(M)$. This not only allows us to relate topological dynamical systems to linear dynamical systems but also provide a new class of hypercyclic operators acting on Lipschitz-free spaces.
