| Contents |
| In this talk we describe some dynamical properties of a Morse decomposition with a countable number of sets.
We prove that the dynamically gradient dynamics of Morse sets together with a separation assumption is equivalent to the existence of an ordered Lyapunov function associated to the Morse sets and also to the existence of a Morse decomposition (that is, the global attractor can be described as an increasing family of local attractors and their associated repellers).
This theory generalizes the well known classical results, in which a finite number of components is considered, and is illustrated with a suitable application. |
|