An algebraic-topological approach to dynamical systems and symplectic topology
Sufficient conditions for the realization of Lyapunov graphs as Gutierrez-Sotomayo...
Transition Matrices associated with the Morse-Witten Complex
| Full text | |
| Author(s): |
Lima, D. V. S.
;
Da Silveira, M. R.
;
Vieira, E. R.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Ergodic Theory and Dynamical Systems; v. N/A, p. 33-pg., 2022-02-21. |
| Abstract | |
In this paper we apply Conley index theory in a covering space of an invariant set S, possibly not isolated, in order to describe the dynamics in S. More specifically, we consider the action of the covering translation group in order to define a topological separation of S which distinguishes the connections between the Morse sets within a Morse decomposition of S. The theory developed herein generalizes the classical connection matrix theory, since one obtains enriched information on the connection maps for non-isolated invariant sets, as well as for isolated invariant sets. Moreover, in the case of an infinite cyclic covering induced by a circle-valued Morse function, one proves that the Novikov differential of f is a particular case of the p-connection matrix defined herein. (AU) | |
| FAPESP's process: | 16/24707-4 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 20/11326-8 - An algebraic-topological approach to dynamical systems and symplectic topology |
| Grantee: | Dahisy Valadão de Souza Lima |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |