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

Redei, Miklos and Werndl, Charlotte (2011) On the history of the isomorphism problem of dynamical systems with special regard to von Neumann's contribution. [Preprint]

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    Abstract

    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 In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial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.


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    Item Type: Preprint
    Additional Information: Forthcoming in: Archive for History of Exact Sciences
    Keywords: isomorphism problem, von Neumann, spectral theory, ergodic theory, dynamical systems
    Subjects: Specific Sciences > Physics > Classical Physics
    Specific Sciences > Mathematics
    Depositing User: Charlotte Werndl
    Date Deposited: 28 Sep 2011 09:09
    Last Modified: 28 Sep 2011 09:09
    Item ID: 8813
    URI: http://philsci-archive.pitt.edu/id/eprint/8813

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