An attraction result and an index theorem for continuous flows on $ℝ^n × [0,∞)$

Klaudiusz Wójcik

An attraction result and an index theorem for continuous flows on

ℝ^{n} \times [0, \infty)

Klaudiusz Wójcik

Annales Polonici Mathematici, Tome 66 (1997), p. 203-211 / Harvested from The Polish Digital Mathematics Library

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Résumé

We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on $E = ℝ^{n + 1}$ for which $\partial E = ℝ^{n} \times 0$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^{n} \times [0, \infty)$ .

Publié le : 1997-01-01

Zbl 0873.58054

EUDML-ID : urn:eudml:doc:269989

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Klaudiusz Wójcik. An attraction result and an index theorem for continuous flows on $ℝ^n × [0,∞)$
            . Annales Polonici Mathematici, Tome 66 (1997) pp. 203-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv65z3p203bwm/

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