The continuation theory for Morse decompositions and connection matrices
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- by Robert D. Franzosa PDF
- Trans. Amer. Math. Soc. 310 (1988), 781-803 Request permission
Abstract:
The continuation theory for ($<$-ordered) Morse decompositions and the indices defined on them—the homology index braid and the connection matrices—is established. The equivalence between $<$-ordered Morse decompositions and $<$-consistent attractor filtrations is displayed. The spaces of ($<$-ordered) Morse decompositions for a product parametrization of a local flow are introduced, and the local continuation of ($<$-ordered) Morse decompositions is obtained via the above-described equivalence and the local continuation of attractors. The homology index braid and the connection matrices of an admissible ordering of a Morse decomposition are shown to be invariant on path components of the corresponding space of $<$-ordered Morse decompositions. This invariance is used to prove that the collection of connection matrices of a Morse decomposition is upper semicontinuous over the space of Morse decompositions (and over the parameter space) under local continuation.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 310 (1988), 781-803
- MSC: Primary 58F25; Secondary 34C35, 58F12, 58F14
- DOI: https://doi.org/10.1090/S0002-9947-1988-0973177-6
- MathSciNet review: 973177