Homotopical dynamics II : Hopf invariants, smoothings and the Morse complex
Octavian Cornea (2002)
Annales scientifiques de l'École Normale Supérieure
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Octavian Cornea (2002)
Annales scientifiques de l'École Normale Supérieure
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Schütz, D. (2002)
Algebraic & Geometric Topology
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Roman Srzednicki (1999)
Banach Center Publications
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The Conley index theory was introduced by Charles C. Conley (1933-1984) in [C1] and a major part of the foundations of the theory was developed in Ph. D. theses of his students, see for example [Ch, Ku, Mon]. The Conley index associates the homotopy type of some pointed space to an isolated invariant set of a flow, just as the fixed point index associates an integer number to an isolated set of fixed points of a continuous map. Examples of isolated invariant sets arise naturally in the...
E.N. Dancer (1984)
Journal für die reine und angewandte Mathematik
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Andrei Vladimirovich Pazhitnov (1995)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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K. Gęba, M. Izydorek, A. Pruszko (1999)
Studia Mathematica
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We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals...
E.N. Dancer (1987)
Journal für die reine und angewandte Mathematik
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Marian Mrozek, James Reineck, Roman Srzednicki (1999)
Banach Center Publications
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In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain...
Gaucher, Philippe (2005)
The New York Journal of Mathematics [electronic only]
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Daniel C. Isaksen (2002)
Fundamenta Mathematicae
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We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning strict pro-maps are essential for a theorem about étale homotopy types. We also correct some mistakes in the literature on this topic.