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Transactions of the American Mathematical Society

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An index for periodic orbits
of local semidynamical systems

Author: Christian C. Fenske
Journal: Trans. Amer. Math. Soc. 350 (1998), 4973-4991
MSC (1991): Primary 54H20; Secondary 58F25, 58F32, 55M25
MathSciNet review: 1458322
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Abstract: We define an index of Fuller type counting the number of periodic orbits of a semiflow on an ANR by a suitable approximation process.

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  • [CMP] S.N. Chow and J. Mallet-Paret, The Fuller index and global Hopf bifurcation, J. Differential Equations 39 (1978), 66 - 84. MR 58:11665
  • [DT] N. Dancer and J.F. Toland, Degree theory for orbits of prescribed period of flows with a first integral, Proc. London Math. Soc. 60 (1990), 549 - 580. MR 91a:58152
  • [Du] J. Dugundji, Topology, Allyn and Bacon, Boston, 1978. MR 57:17581
  • [F1] C.C. Fenske, Periodic orbits of semiflows - Local indices and sections, Selected Topics in Operations Research and Mathematical Economics. Proceedings, Karlsruhe 1984 (G. Hammer and D. Pallaschke, eds.), Lecture Notes in Economics and Mathematical Systems 226, Springer, Berlin/Heidelberg/New York, 1984, pp. 348-360. MR 86i:54035
  • [F2] -, A simple-minded approach to the index of periodic orbits, J. Math. Anal. Appl. 129 (1988), 517-532. MR 89g:54098
  • [F3] -, An index for periodic orbits of functional differential equations, Math. Ann. 285 (1989), 381-392. MR 90m:34135
  • [Fu] F.B. Fuller, An index of fixed point type for periodic orbits, Amer. J. Math. 89 (1967), 133-148. MR 35:497
  • [GN] R. Geoghegan and A. Nicas, Trace and torsion in the theory of flows, Topology 33 (1994), 683-719. MR 95h:55002
  • [G] J. Girolo, Approximating compact sets in normed spaces, Pacific J. Math. 98 (1982), 81-89. MR 83c:54046
  • [H] S.-T. Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 31:6202
  • [M] W.S. Massey, Homology and Cohomology Theory, Marcel Dekker, New York/Basel, 1978. MR 58:7594
  • [P1] A.J.B. Potter, On a generalization of the Fuller index, Nonlinear functional analysis and its applications (Felix Browder, ed.), Proc. Symp. Pure Math. 45, Part 2, AMS, Providence, 1986, pp. 283-286. MR 87g:47112
  • [P2] -, Approximation methods and the generalised Fuller index for semi-flows in Banach spaces, Proc. Edinburgh Math. Soc. 29 (1986), 299-308. MR 87m:47121
  • [Sr1] R. Srzednicki, Periodic orbit indices, Fund. Math 135 (1990), 147-173. MR 91m:54054
  • [Sr2] -, Topological invariants and detection of periodic orbits, J. Differential Equations 111 (1994), 283-298. MR 95g:58186

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Additional Information

Christian C. Fenske
Affiliation: Mathematisches Institut der Justus-Liebig, Universität Arndtstrasse, 2 D-35392 Giessen, Germany

Keywords: Index, periodic orbit, semiflow, Fuller index, functional differential equation
Received by editor(s): November 20, 1995
Received by editor(s) in revised form: November 19, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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