| Texto completo | |
| Autor(es): |
Lima, D. V. S.
;
De Rezende, K. A.
;
Da Silveira, M. R.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Ergodic Theory and Dynamical Systems; v. N/A, p. 49-pg., 2023-05-25. |
| Resumo | |
In this work, we explore the dynamical implications of a spectral sequence analysis of a filtered chain complex associated to a non-singular Morse-Smale (NMS) flow ? on a closed orientable 3-manifold M-3 with no heteroclinic trajectories connecting saddle periodic orbits. We introduce the novel concepts of cancellations and reductions of pairs of periodic orbits based on Franks' morsification and Smale's cancellation theorems. The main goal is to establish an algebraic-dynamical correspondence between the unfolding of this spectral sequence associated to ? and a family of flows obtained by cancelling and reducing pairs of periodic orbits of ? on M-3. This correspondence is achieved through a spectral sequence sweeping algorithm (SSSA), which determines the order in which these cancellations and reductions of periodic orbits occur, producing a family of NMS flows that reaches a core flow when the spectral sequence converges. (AU) | |
| Processo FAPESP: | 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos |
| Beneficiário: | Marco Antônio Teixeira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 16/24707-4 - Topologia algébrica, geométrica e diferencial |
| Beneficiário: | Daciberg Lima Gonçalves |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 20/11326-8 - Uma abordagem algébrica-topológica para sistemas dinâmicos e topologia simplética |
| Beneficiário: | Dahisy Valadão de Souza Lima |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |