We study the shape (in the sense of Borsuk) of attractors of continuous semidynamical systems on general metric spaces. We show, in particular, that the natural inclusion of the global attractor into the state space is a shape equivalence. This and other results of the paper are used to develop an elementary Morse theory of an attractor.
|Original language||English (US)|
|Number of pages||25|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Jan 1 2000|
All Science Journal Classification (ASJC) codes
- Applied Mathematics