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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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Connected simple systems and the Conley index of isolated invariant sets
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by Dietmar Salamon PDF
Trans. Amer. Math. Soc. 291 (1985), 1-41 Request permission

Abstract:

The object of this paper is to present new and simplified proofs for most of the basic results in the index theory for flows. Simple, explicit formulae are derived for the maps which play a central role in the theory. The presentation is self-contained.
References
  • N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Die Grundlehren der mathematischen Wissenschaften, Band 161, Springer-Verlag, New York-Berlin, 1970. MR 0289890
  • George D. Birkhoff, Dynamical systems, American Mathematical Society Colloquium Publications, Vol. IX, American Mathematical Society, Providence, R.I., 1966. With an addendum by Jurgen Moser. MR 0209095
  • 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
  • C. C. Conley and R. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian systems, Mathematics Research Center, University of Wisconsin-Madison, TSR #2567, 1983; Comm. Pure Appl. Math. 37 (1984). R. Franzosa, Index filtrations and connection matrices for partially ordered Morse decompositions, Ph. D. Thesis, University of Wisconsin-Madison, 1984.
  • 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
  • Henry L. Kurland, Homotopy invariants of repeller-attractor pairs. II. Continuation of R-A pairs, J. Differential Equations 49 (1983), no. 2, 281–329. MR 708647, DOI 10.1016/0022-0396(83)90016-5
  • John Montgomery, Cohomology of isolated invariant sets under perturbation, J. Differential Equations 13 (1973), 257–299. MR 334173, DOI 10.1016/0022-0396(73)90018-1
  • K. P. Rybakowski and E. Zehnder, A Morse equation in Conley’s index theory for semiflows on metric spaces, Institut fur Mathematik, Ruhr Universität Bochum, 1982.
  • 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
  • Edwin H. Spanier, Algebraic topology, Springer-Verlag, New York-Berlin, 1981. Corrected reprint. MR 666554
  • George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 291 (1985), 1-41
  • MSC: Primary 58F25; Secondary 34C35
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0797044-3
  • MathSciNet review: 797044