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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Shift equivalence and the Conley index
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by John Franks and David Richeson PDF
Trans. Amer. Math. Soc. 352 (2000), 3305-3322 Request permission

Abstract:

In this paper we introduce filtration pairs for an isolated invariant set of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an invariant of the isolated invariant set. Moreover, the maps defining the shift equivalence can be chosen canonically. Last, we define partially ordered Morse decompositions and prove the existence of Morse set filtrations for such decompositions.
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Additional Information
  • John Franks
  • Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
  • MR Author ID: 68865
  • Email: john@math.nwu.edu
  • David Richeson
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48023-1027
  • MR Author ID: 642588
  • ORCID: setImmediate$0.3081954432672045$9
  • Email: richeson@math.msu.edu
  • Received by editor(s): June 22, 1998
  • Published electronically: March 24, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 3305-3322
  • MSC (2000): Primary 37B30
  • DOI: https://doi.org/10.1090/S0002-9947-00-02488-0
  • MathSciNet review: 1665329