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Transactions of the American Mathematical Society

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On arbitrary sequences of isomorphisms in $ R\sp{m}\rightarrow R\sp{m}$


Author: Charles C. Pugh
Journal: Trans. Amer. Math. Soc. 184 (1973), 387-400
MSC: Primary 58F10
MathSciNet review: 0326778
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Abstract: In this paper a new, clean proof of an algebraic theorem needed in ordinary differential equations is presented. The theorem involves the existence and uniqueness of a ``complete splitting'' for some subsequence of an arbitrary sequence of isomorphisms of Euclidean m-space. In the positive-definite case, a complete splitting is a limit condition on eigenspaces and eigenvalues.


References [Enhancements On Off] (What's this?)

  • [1] G. Mostow, Lectures on Lie groups and Lie algebras, Lecture 32, Yale University, New Haven, Conn.
  • [2] Charles C. Pugh, The closing lemma, Amer. J. Math. 89 (1967), 956–1009. MR 0226669

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DOI: https://doi.org/10.1090/S0002-9947-1973-0326778-1
Article copyright: © Copyright 1973 American Mathematical Society