The Conley index for flows preserving generalized symmetries
Pruszko, Artur
Banach Center Publications, Tome 50 (1999), p. 193-217 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:208933 
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     title = {The Conley index for flows preserving generalized symmetries},
     journal = {Banach Center Publications},
     volume = {50},
     year = {1999},
     pages = {193-217},
     zbl = {0946.37012},
     language = {en},
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Pruszko, Artur. The Conley index for flows preserving generalized symmetries. Banach Center Publications, Tome 50 (1999) pp. 193-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv47i1p193bwm/

[000] [B] T. Bartsch, Topological Methods for Variational Problems with Symmetries, Springer, Berlin 1993. | Zbl 0789.58001

[001] [C] C. C. Conley, Isolated Invariant Sets and Morse Index, CBMS Regional Confer. Ser. in Math., Amer. Math. Soc., Providence, R.I., 1978. | Zbl 0397.34056

[002] [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. | Zbl 0559.58019

[003] [E] R. Engelking, General Topology, PWN, Warsaw 1977.

[004] [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. | Zbl 0633.58040

[005] [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. | Zbl 0694.58017

[006] [G] K. Gęba, Degree for Gradient Equivariant Maps and Equivariant Conley Index, Topological Nonlinear Analysis II, Birkhäuser, Boston - Basel - Berlin 1997, 247-272. | Zbl 0880.57015

[007] [M] K. Mischaikow, Conley Index Theory, Lect. Notes in Math. 1609, 119-207, Springer, Berlin 1995. | Zbl 0847.58062

[008] [RS] J. Robbin and D. Salamon, Dynamical Systems, Shape Theory and the Conley Index, Ergod. Th. and Dynam. Syst. 8* (1988), 375-393. | Zbl 0682.58040

[009] [R] K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer, Berlin 1987. | Zbl 0628.58006

[010] [S] D. Salamon, Connected Simple Systems and the Conley Index of Isolated Invariant Sets, Trans. Amer. Math. Soc. 291 (1985), 1-41. | Zbl 0573.58020

[011] [Sz] A. Szymczak, The Conley Index for Discrete Semidynamical Systems, Top. Appl. 66 (1995), 215-240. | Zbl 0840.34043

[012] [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. | Zbl 0032.35001

[013] [Wh] G. W. Whitehead, Elements of Homotopy Theory, Springer, New York 1978.