Conley index and permanence in dynamical systems (Q1284668)

The main task of the present paper is to show that if \(S\subset\mathbb{R}^n\times\{0\}\) is an isolated set with nonzero homological Conley idex, then there exists an \(x\) in \(\mathbb{R}^n \times (0,\infty)\) such that \(\omega(x)\) is contained in \(S\). This may be understood as a strong violation of permanence. The results can be applied to a problem coming from permanence theory, which plays an important role in mathematical ecology.