| Full text | |
| Author(s): |
Montufar, H.
;
De Rezende, K. A.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF SINGULARITIES; v. 22, p. 37-pg., 2020-01-01. |
| Abstract | |
In [6], a characterization and genericity theorem for C-1-structurally stable vector fields tangent to a 2-dimensional compact subset M of R-k are established. Also in [6], new types of structurally stable singularities and periodic orbits are presented. In this work we study the continuous flows associated to these vector fields, which we refer to as the Gutierrez-Sotomayor flows on manifolds M with simple singularities, GS flows, by using Conley Index Theory. The Conley indices of all simple singularities are computed and an Euler characteristic formula is obtained. By considering a stratification of M which decomposes it into a union of its regular and singular strata, certain Euler type formulas which relate the topology of M and the dynamics on the strata are obtained. The existence of a Lyapunov function for GS flows without periodic orbits and singular cycles is established. Using long exact sequence analysis of index pairs we determine necessary and sufficient conditions for a GS flow to be defined on an isolating block. We organize this information combinatorially with the aid of Lyapunov graphs and using a Poincare-Hopf equality we construct isolating blocks for all simple singularities. (AU) | |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |