论文标题
阴影，有限的订单偏移和超规模空间
Shadowing, Finite Order Shifts and Ultrametric Spaces
论文作者
论文摘要
受到良好和梅尔多的新颖作品的启发，我们建立了阴影，有限订单变化和超级完整空间之间的基本联系。我们发展了无限字母有限类型的转移理论。我们称它们为有限订单的班次。我们发展了一般度量空间中阴影特性的基本理论，在紧凑空间中表现出与理论的相似性和差异。我们将这两种理论连接在零维的完整空间的设置中，表明超级完整空间的均匀连续映射具有有限的阴影属性，并且只有当它是满足Mittag-Leffler条件的有限顺序偏移系统的相反限制。此外，在这种情况下，我们表明阴影属性等同于有限的阴影属性和在系统的反限制描述中满足Mittag-Leffler条件。作为推论，我们获得了超规模空间中的各种地图具有阴影属性，例如相似性，更普遍地是地图，这些地图本身或它们的倒置具有Lipschitz Consent 1。最后，我们将结果应用于$ p $ addic Integers和$ p $ $ p $ adadic的动态。
Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a theory of shifts of finite type for infinite alphabets. We call them shifts of finite order. We develop the basic theory of the shadowing property in general metric spaces, exhibiting similarities and differences with the theory in compact spaces. We connect these two theories in the setting of zero-dimensional complete spaces, showing that a uniformly continuous map of an ultrametric complete space has the finite shadowing property if, and only if, it is an inverse limit of a system of shifts of finite order satisfying the Mittag-Leffler Condition. Furthermore, in this context, we show that the shadowing property is equivalent to the finite shadowing property and the fulfillment of the Mittag-Leffler Condition in the inverse limit description of the system. As corollaries, we obtain that a variety of maps in ultrametric spaces have the shadowing property, such as similarities and, more generally, maps which themselves, or their inverses, have Lipschitz constant 1. Finally, we apply our results to the dynamics of $p$-adic integers and $p$-adic rationals.
