An attraction result and an index theorem for continuous flows on $ℝ^n × [0,∞)$
Volume 65 / 1997
Annales Polonici Mathematici 65 (1997), 203-211
DOI: 10.4064/ap-65-3-203-211
Abstract
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 $∂E = ℝ^n × {0}$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in E\∂E such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^n × [0,∞)$.
