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Wybrane publikacje

  • Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces


    In this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...

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  • Equivariant Morse equation

    The paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.

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  • Morse inequalities via Conley index theory

    The relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.

Uzyskane stopnie/tytuły naukowe

  • 2010-04-16

    Nadanie stopnia naukowego

    dr Matematyka (Dziedzina nauk matematycznych)
    Instytut Matematyczny PAN

wyświetlono 2282 razy