| Full text | |
| Author(s): |
Bertolim, Maria A.
;
De Rezende, Ketty A.
;
Mello, Margarida P.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 65, n. 2, p. 55-pg., 2025-12-01. |
| Abstract | |
. In this paper, we address both a combinatorial continuation question via Lyapunov graphs and the attainability of a preassigned level set, dubbed ground level set and given by its Betti numbers, within a morsification process of a dynamical configuration. The novelty introduced here is a componentwise Lyapunov graph morsification that keeps track of level sets during the morsification process subject to the minimality of the total number of singularities of a morsified flow. The algorithm behind the morsification translates into a system of linear equations whose feasibility is linked to that of a set of inequalities, called componentwise Poincare<acute accent>- Hopf inequalities, involving the input data. This investigation combines techniques from both homological Conley index and network flow theories. (AU) | |
| FAPESP's process: | 22/16455-6 - Algebraic, geometric, and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |