Index filtrations and the homology index braid for partially ordered Morse decompositions
HTML articles powered by AMS MathViewer
- by Robert Franzosa
- Trans. Amer. Math. Soc. 298 (1986), 193-213
- DOI: https://doi.org/10.1090/S0002-9947-1986-0857439-7
- PDF | Request permission
Abstract:
On a Morse decomposition of an invariant set in a flow there are partial orderings defined by the flow. These are called admissible orderings of the Morse decomposition. The index filtrations for a total ordering of a Morse decomposition are generalized in this paper with the definition and proof of existence of index filtrations for admissible partial orderings of a Morse decomposition. It is shown that associated to an index filtration there is a collection of chain complexes and chain maps called the chain complex braid of the index filtration. The homology index braid of the corresponding admissible ordering of the Morse decomposition is obtained by passing to homology in the chain complex braid.References
- Charles Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Mathematics, vol. 38, American Mathematical Society, Providence, R.I., 1978. MR 511133
- Charles Conley and Eduard Zehnder, Morse-type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math. 37 (1984), no. 2, 207–253. MR 733717, DOI 10.1002/cpa.3160370204 R. D. Franzosa, Index filtrations and connection matrices for partially ordered Morse decompositions, Ph. D. Dissertation, Univ. of Wisconsin, Madison, 1984. —, The connection matrix theory for Morse decompositions (in preparation). —, The continuation theory for connection matrices and Morse decompositions (in preparation).
- Henry L. Kurland, The Morse index of an isolated invariant set is a connected simple system, J. Differential Equations 42 (1981), no. 2, 234–259. MR 641650, DOI 10.1016/0022-0396(81)90028-0
- Henry L. Kurland, Homotopy invariants of repeller-attractor pairs. I. The Puppe sequence of an R-A pair, J. Differential Equations 46 (1982), no. 1, 1–31. MR 677580, DOI 10.1016/0022-0396(82)90106-1 —, Homotopy invariants of a repeller-attractor pair. II: Continuation of R-A pairs, J. Differential Equations 49 (1983).
- Dietmar Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc. 291 (1985), no. 1, 1–41. MR 797044, DOI 10.1090/S0002-9947-1985-0797044-3
- Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 298 (1986), 193-213
- MSC: Primary 58F12; Secondary 58E05, 58F25
- DOI: https://doi.org/10.1090/S0002-9947-1986-0857439-7
- MathSciNet review: 857439