The Conley index for flows preserving generalized symmetries

Artur Pruszko

Banach Center Publications (1999)

  • Volume: 47, Issue: 1, page 193-217
  • ISSN: 0137-6934

Abstract

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Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.

How to cite

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Pruszko, Artur. "The Conley index for flows preserving generalized symmetries." Banach Center Publications 47.1 (1999): 193-217. <http://eudml.org/doc/208933>.

@article{Pruszko1999,
abstract = {Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.},
author = {Pruszko, Artur},
journal = {Banach Center Publications},
keywords = {generalized symmetry; group action; isolated invariant set; Conley index},
language = {eng},
number = {1},
pages = {193-217},
title = {The Conley index for flows preserving generalized symmetries},
url = {http://eudml.org/doc/208933},
volume = {47},
year = {1999},
}

TY - JOUR
AU - Pruszko, Artur
TI - The Conley index for flows preserving generalized symmetries
JO - Banach Center Publications
PY - 1999
VL - 47
IS - 1
SP - 193
EP - 217
AB - Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.
LA - eng
KW - generalized symmetry; group action; isolated invariant set; Conley index
UR - http://eudml.org/doc/208933
ER -

References

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  1. [B] T. Bartsch, Topological Methods for Variational Problems with Symmetries, Springer, Berlin 1993. Zbl0789.58001
  2. [C] C. C. Conley, Isolated Invariant Sets and Morse Index, CBMS Regional Confer. Ser. in Math., Amer. Math. Soc., Providence, R.I., 1978. Zbl0397.34056
  3. [CZ] C. C. Conley and E. Zehnder, A Morse Type Index Theory for Flows and Periodic Solutions to Hamiltonian Systems, Comm. Pure Appl. Math. 37 (1984), 207-253. Zbl0559.58019
  4. [E] R. Engelking, General Topology, PWN, Warsaw 1977. 
  5. [F] A. Floer, A Refinement of the Conley Index and an Application to the Stability of Hyperbolic Invariant Sets, Ergod. Th. and Dynam. Syst. 7 (1988), 93-103. Zbl0633.58040
  6. [FZ] A. Floer and E. Zehnder, The Equivariant Conley Index and Bifurcation of Periodic Solution of Hamiltonian Systems, Ergod. Th. and Dynam. Syst. 8* (1988), 87-97. Zbl0694.58017
  7. [G] K. Gęba, Degree for Gradient Equivariant Maps and Equivariant Conley Index, Topological Nonlinear Analysis II, Birkhäuser, Boston - Basel - Berlin 1997, 247-272. Zbl0880.57015
  8. [M] K. Mischaikow, Conley Index Theory, Lect. Notes in Math. 1609, 119-207, Springer, Berlin 1995. Zbl0847.58062
  9. [RS] J. Robbin and D. Salamon, Dynamical Systems, Shape Theory and the Conley Index, Ergod. Th. and Dynam. Syst. 8* (1988), 375-393. Zbl0682.58040
  10. [R] K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer, Berlin 1987. Zbl0628.58006
  11. [S] D. Salamon, Connected Simple Systems and the Conley Index of Isolated Invariant Sets, Trans. Amer. Math. Soc. 291 (1985), 1-41. Zbl0573.58020
  12. [Sz] A. Szymczak, The Conley Index for Discrete Semidynamical Systems, Top. Appl. 66 (1995), 215-240. Zbl0840.34043
  13. [W] T. Ważewski, Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles, Ann. Soc. Polon. Math. 20 (1947), 249-313. Zbl0032.35001
  14. [Wh] G. W. Whitehead, Elements of Homotopy Theory, Springer, New York 1978. 

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