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): |
Lima, Dahisy V. de S.
[1]
;
Manzoli Neto, Oziride
[2]
;
de Rezende, Ketty A.
[1]
;
da Silveira, Mariana R.
[3]
Total Authors: 4
|
| Affiliation: | [1] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil
[2] Univ Sao Paulo, ICMC, Sao Carlos, SP - Brazil
[3] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 51, n. 1, p. 259-311, MAR 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
A spectral sequence analysis of a filtered Novikov complex (N-{*}(f), Delta) over Z ((t)) is developed with the goal of obtaining results relating the algebraic and dynamical settings. Specifically, the unfolding of a spectral sequence of (N-{*}(f), Delta) and the cancellation of its modules is associated to a one parameter family of circle-valued Morse functions on a surface and the dynamical cancellations of its critical points. The data of a spectral sequence computed for (N-{*}(f), Delta) is encoded in a family of matrices Delta(r) produced by the Spectral Sequence Sweeping Algorithm (SSSA), which has as its initial input the differential Delta. As one ``turns the pages{''} of the spectral sequence, differentials which are isomorphisms produce cancellation of pairs of modules. Corresponding to these cancellations, a family of circle-valued Morse functions f(r) is obtained by successively removing the corresponding pairs of critical points of f. We also keep track of all dynamical information on the birth and death of connecting orbits between consecutive critical points, as well as periodic orbits that arise within a family of negative gradient flows associated to f(r). (AU) | |
| FAPESP's process: | 15/10930-0 - Symplectic dynamics and spectral sequences |
| Grantee: | Dahisy Valadão de Souza Lima |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 14/11943-6 - Spectral sequences for Morse-Bott and Morse-Novikov flows study |
| Grantee: | Dahisy Valadão de Souza Lima |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |