| Full text | |
| Author(s): |
Bertolim, Maria Alice
;
Mello, Margarida Pinheiro
;
Rezende, Ketty Abaroa de
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Ergodic Theory and Dynamical Systems; v. 25, n. 1, p. 1-39, Feb. 2005. |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics |
| Abstract | |
Lyapunov graphs carry dynamical information of gradient-like flows as well as topological information of their phase space which is taken to be a closed orientable n-manifold. In this paper we will show that an abstract Lyapunov graph L(h(0), . . . , h(n), kappa) in dimension n greater than 2, with cycle number kappa, satisfies the Poincare-Hopf inequalities if and only if it satisfies the Morse inequalities and the first Betti number, gamma(1), is greater than or equal to kappa. We also show a continuation theorem for abstract Lyapunov graphs with the presence of cycles. Finally, a family of Lyapunov graphs L(h(0), . . . , h(n), kappa) with fixed pre-assigned data (h(0), . . . , h(n), kappa) is associated with the Morse polytope, P-kappa(h(0), . . . , h(n)), determined by the Morse inequalities for the given data. (AU) | |
| FAPESP's process: | 01/04597-4 - Computational Methods in Optimization |
| Grantee: | José Mário Martinez Perez |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 02/10246-2 - Control systems, dynamical systems, stochastic dynamical systems, Lie theory and differential geometry |
| Grantee: | Luiz Antonio Barrera San Martin |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 00/05385-8 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |