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1999 | 47 | 1 | 193-217
Tytuł artykułu

The Conley index for flows preserving generalized symmetries

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
47
Numer
1
Strony
193-217
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland
Bibliografia
  • [B] T. Bartsch, Topological Methods for Variational Problems with Symmetries, Springer, Berlin 1993.
  • [C] C. C. Conley, Isolated Invariant Sets and Morse Index, CBMS Regional Confer. Ser. in Math., Amer. Math. Soc., Providence, R.I., 1978.
  • [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.
  • [E] R. Engelking, General Topology, PWN, Warsaw 1977.
  • [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.
  • [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.
  • [G] K. Gęba, Degree for Gradient Equivariant Maps and Equivariant Conley Index, Topological Nonlinear Analysis II, Birkhäuser, Boston - Basel - Berlin 1997, 247-272.
  • [M] K. Mischaikow, Conley Index Theory, Lect. Notes in Math. 1609, 119-207, Springer, Berlin 1995.
  • [RS] J. Robbin and D. Salamon, Dynamical Systems, Shape Theory and the Conley Index, Ergod. Th. and Dynam. Syst. 8* (1988), 375-393.
  • [R] K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer, Berlin 1987.
  • [S] D. Salamon, Connected Simple Systems and the Conley Index of Isolated Invariant Sets, Trans. Amer. Math. Soc. 291 (1985), 1-41.
  • [Sz] A. Szymczak, The Conley Index for Discrete Semidynamical Systems, Top. Appl. 66 (1995), 215-240.
  • [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.
  • [Wh] G. W. Whitehead, Elements of Homotopy Theory, Springer, New York 1978.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv47i1p193bwm
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