| Full text | |
| Author(s): |
Weber, Joa
Total Authors: 1
|
| Document type: | Journal article |
| Source: | TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 47, n. 2, p. 641-646, JUN 2016. |
| Web of Science Citations: | 1 |
| Abstract | |
We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points. More precisely, we interpret the stable fibrations of certain Conley pairs (N, L), established in {[}2], as a dynamical thickening of the stable manifold. As a first application and to illustrate efficiency of the concept we reprove a fundamental theorem of classical Morse theory, Milnor's homotopical cell attachment theorem {[}1]. Dynamical thickening leads to a conceptually simple and short proof. (AU) | |
| FAPESP's process: | 13/20912-4 - Infinite dimensional hyperbolic dynamics |
| Grantee: | Joachim Weber |
| Support Opportunities: | Regular Research Grants |