Article ID: CBB001220402

On the History of the Isomorphism Problem of Dynamical Systems with Special Regard to Von Neumann's Contribution (2012)

unapi

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 In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this article clarifies von Neumann's contribution to discovering the relationship between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

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https://data.isiscb.org/isis/citation/CBB001220402/

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Authors & Contributors
Rédei, Miklós
Rossi, Andrea
Morandi, Adriano
Von Neumann, John
Stöltzner, Michael
Rowe, David E.
Concepts
Mathematics
Mathematical physics
Physics
Economics
National histories
Quantum mechanics
Time Periods
20th century
19th century
20th century, early
Places
United States
Italy
Milan (Italy)
Scandinavia; Nordic countries
Poland
Institutions
Institute for Advanced Study (Princeton, N.J.)
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