Lusternik-Schnirelmann Theory for a Morse Decomposition
| dc.creator | Razvan, M. R. | |
| dc.date | 2000-09-26 | |
| dc.date.accessioned | 2026-07-07T04:37:41Z | |
| dc.date.available | 2026-07-07T04:37:41Z | |
| dc.description | Let $ϕ^t$ be a continuous flow on a metric space $X$ and $I$ be an isolated invariant set with an index pair $(N,L)$ and a Morse decomposition $\{M_i\}^n_{i=1}$. For every category $ν$ on $N/L$, we prove that $ν(N/L)\leq ν([L])+\sum_{i=1}^n ν(M_i)$. As a result if $ϕ^t|_I$ is gradient-like and $X$ is semi-locally contractible, then $ϕ^t$ has at least $ν_H(h(I))-1$ rest points in $I$ where $h(I)$ is the Conley index of $I$ and $ν_H$ is the Homotopy Lusternik-Schnirelmann category. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0009224 | |
| dc.identifier | http://arxiv.org/abs/math/0009224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59996 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 54H20, 55M30 | |
| dc.title | Lusternik-Schnirelmann Theory for a Morse Decomposition | |
| dc.type | text |