发表机构
APJ Abdul Kalam Technological University; Rajagiri School of Engineering and Technology; Muthoot Institute of Technology and Science（阿卜杜勒·卡拉姆技术大学; 拉吉吉里工程技术学院; 穆托特科技与工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出时间度量空间框架，通过轨迹空间上的区间依赖度量刻画连续演化域，并发展时间迭代函数系统理论，证明吸引子随动力学协同演化且保持稳定。
AI 中文摘要
我们引入时间度量空间，这是一个用于形式化连续演化域上的度量与拓扑结构的框架。我们并非在固定空间上定义单一度量，而是在关联的轨迹空间上构造一族依赖于时间区间的度量，从而能够度量有限时间区间内连续轨迹之间的距离。我们建立了轨迹空间的基本拓扑，证明其从底层度量空间继承完备性，并发展了相应的时间超空间及其完备性。最后，我们发展了作用于这些演化空间上的迭代函数系统理论，证明其吸引子与底层动力学协同演化，并且即使演化几何导致生成映射失去经典压缩性质，吸引子仍保持稳定。
英文摘要
We introduce temporal metric spaces, a framework for formalizing metric and topological structures on continuously evolving domains. Rather than defining a single metric on a fixed space, we construct a family of interval-dependent metrics on an associated trajectory space, enabling distances to be measured between continuous trajectories over finite time intervals. We establish the fundamental topology of the trajectory space, prove that it inherits completeness from the underlying metric space, and develop the corresponding temporal hyperspace together with its completeness. Finally, we develop a theory of iterated function systems acting on these evolving spaces, proving that their attractors evolve coherently with the underlying dynamics and remain stable even when the evolving geometry causes the generating mappings to lose their classical contraction property.
Comments25 pages, 2 figures
