标题： 关于动力系统同构问题的历史，特别关注冯·诺伊曼的贡献 显示英文标题

标题： On the history of the isomorphism problem of dynamical systems with special regard to von Neumann's contribution

摘要： 本文回顾了动力系统理论（遍历理论）中空间同构问题历史上的几个主要事件。 特别是，通过系统地并结合历史背景分析约翰·冯·诺伊曼于1941年写给斯坦尼斯拉夫·乌拉姆的一封此前未发表的信件，本文澄清了冯·诺伊曼在发现空间同构与谱同构之间关系方面的贡献。 本文的主要观点是，冯·诺伊曼在其给乌拉姆的信中描述的论证是第一个证明空间同构与谱同构不等价的证明，因为谱同构比空间同构更弱：冯·诺伊曼表明，具有混合谱的谱同构遍历动力系统未必是空间同构的。 显示英文摘要

摘要： This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory (ergodic theory). In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to Ulam is the very first proof that spatial isomorphism and spectral isomorphism are not equivalent because spectral isomorphism is weaker than spatial isomorphism: von Neumann shows that spectrally isomorphic ergodic dynamical systems with mixed spectra need not be spatially isomorphic.