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

Rédei, Miklós and Werndl, Charlotte (2012) On the history of the isomorphism problem of dynamical systems with special regard to von Neumann’s contribution. Archive for History of Exact Sciences, 66 (1). pp. 71-93. ISSN 0003-9519

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Abstract

This article 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 In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this article clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the article 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.

Item Type: Article
Official URL: http://www.springer.com/mathematics/history+of+mat...
Additional Information: © 2012 Springer
Library of Congress subject classification: B Philosophy. Psychology. Religion > BC Logic
Q Science > QA Mathematics
Sets: Departments > Philosophy, Logic and Scientific Method
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 12 Dec 2011 16:27
URL: http://eprints.lse.ac.uk/40283/

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