Artículos de revistas
Dynamic Morse decompositions for semigroups of homeomorphisms and control systems
Fecha
2012-01-01Registro en:
Journal of Dynamical and Control Systems. New York: Springer/plenum Publishers, v. 18, n. 1, p. 1-19, 2012.
1079-2724
10.1007/s10883-012-9132-9
WOS:000302345000001
6796683603864969
Autor
Universidade Estadual de Maringá (UEM)
Universidade Estadual Paulista (Unesp)
Institución
Resumen
In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.