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):71-93 (2012)
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Abstract

This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems 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 In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial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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Author Profiles

Charlotte Sophie Werndl
London School of Economics
Miklós Rédei
London School of Economics

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Are deterministic descriptions and indeterministic descriptions observationally equivalent?Charlotte Werndl - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (3):232-242.
Entropy - A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 115-142.

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