Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/5030
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dc.contributor.authorRybakowski, Krzysztof P.-
dc.date.accessioned2011-07-27T07:40:33Z-
dc.date.available2011-07-27T07:40:33Z-
dc.date.issued1986-
dc.identifier.citationKrzysztof P. Rybakowski, “On critical groups and the homotopy index in Morse theory on Hilbert manifolds”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 18 (1986), pp. 163-176.it_IT
dc.identifier.issn0049-4704-
dc.identifier.urihttp://hdl.handle.net/10077/5030-
dc.description.abstractSia U un aperto nello spazio di Hilbert H, $\varphi\epsilon C^{2-}(U,\mathbf{R)\textrm{,}}\xi\epsilon U$ un punto critico isolato di $\varphi$, e $\pi$il flusso generato dalle soluzioni di $\dot{u}$=-$\triangle\varphi(u)$. Se $\xi$ ha un intorno fortemente ammissibile, allora i gruppi critici di ($\varphi$, $\xi$) nel senso di Rothe sono isomorfi ai gruppi di omologia dell'indice di omotopia di ($\pi,\left\{ \xi\right\} )$ (Teorema 2). Se $\varphi\epsilon C^{2}(U,\mathbf{R})$, $\varphi''(\xi)$ è un'applicazione di Fredholm, ma $\xi$ non ha un intorno fortemente ammissibile, allora tutti i gruppi critici di ($\varphi,\xi)$ sono uguali a zero (banali) (Teorema 4).-
dc.description.abstractLet U be open in the Hilbert space H, $\varphi\epsilon C^{2-}(U,\mathbf{R)\textrm{,}}\xi\epsilon U$ be an isolated criticai point of $\varphi$, and $\pi$ be the flow generated by the solutions of $\dot{u}$=-$\triangle\varphi(u)$. If $\xi$ has a strongly admissible neighborhood, then the critical groups of ($\varphi$, $\xi$) are isomorphic to the homology groups of the homotopy index of ($\pi,\left\{ \xi\right\} )$ (Theorem 2). If $\varphi\epsilon C^{2}(U,\mathbf{R})$, $\varphi''(\xi)$ is a Fredholm operator, but $\xi$ does not have a strongly admissible neighborhood then all critical groups of ($\varphi,\xi)$ are trivial (Theorem 4).-
dc.language.isoenit_IT
dc.publisherUniversità degli Studi di Trieste. Dipartimento di Scienze Matematicheit_IT
dc.relation.ispartofseriesRendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematicsit_IT
dc.relation.ispartofseries18 (1986)it_IT
dc.titleOn critical groups and the homotopy index in Morse theory on Hilbert manifoldsit_IT
dc.typeArticle-
item.openairetypearticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
item.fulltextWith Fulltext-
item.grantfulltextopen-
item.languageiso639-1en-
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.18 (1986)
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