An algebraic-topological approach to dynamical systems and symplectic topology
Spectral sequences for Morse-Bott and Morse-Novikov flows study
The study of the Morse-Witten Complex via Spectral Sequences
| Full text | |
| Author(s): |
Cornea, O.
;
de Rezende, K. A.
;
da Silveira, M. R.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Ergodic Theory and Dynamical Systems; v. 30, p. 46-pg., 2010-08-01. |
| Abstract | |
In this paper, we analyse the dynamics encoded in the spectral sequence (E(r), d(r)) associated with certain Conley theory connection maps in the presence of an 'action' type filtration. More specifically, we present an algorithm for finding a chain complex C and its differential; the method uses a connection matrix Delta to provide a system that spans E(r) in terms of the original basis of C and to identify all of the differentials d(p)(r) : E(p)(r) -> E(p-r)(r). In exploring the dynamical implications of a non-zero differential, we prove the existence of a path that joins the singularities generating E(p)(0) and E(p-r)(0)in the case where a direct connection by a flow line does not exist. This path is made up of juxtaposed orbits of the flow and of the reverse flow, and proves to be important in some applications. (AU) | |
| FAPESP's process: | 02/10246-2 - Control systems, dynamical systems, stochastic dynamical systems, Lie theory and differential geometry |
| Grantee: | Luiz Antonio Barrera San Martin |
| Support Opportunities: | Research Projects - Thematic Grants |