嵌入的全局拓扑
Global Topology from an Embedding
摘要：
混沌数据嵌入到一个合适的相空间创建一个原始的吸引子与重建的吸引子的同构。虽然是同构的，但原始吸引子和重构吸引子可能不是拓扑等价的。在以前的工作中，我们展示了如何原始和重建的吸引子可以不同时，原来的是三维的和genus-one类型。在目前的工作中，我们将这一结果推广到三维吸引子的任意属。这个结果描述了洛伦兹吸引子及其重构所表现出的对称性。
英文摘要：
An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically equivalent. In a previous work we showed how the original and reconstructed attractors can differ when the original is three-dimensional and of genus-one type. In the present work we extend this result to three-dimensional attractors of arbitrary genus. This result describes symmetries exhibited by the Lorenz attractor and its reconstructions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
