Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the history of the isomorphism problem of dynamical systems with
  special regard to von Neumann's contribution   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hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw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.

36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph