Attractor, chain recurrent set and limit set of flow (Q1585589)

The paper deals with the properties of attractors, chain recurrent sets and limit sets of the flow on a compact metric space. The author introduces the notion of recurrence strong chain recurrent and proves that an arbitrary strong chain recurrent set is contained in a chain recurrent set and that an arbitrary non-wandering set is contained in a strong chain recurrent set. Moreover, the author presents a class of dynamical systems for which a strong chain recurrent set is a proper subset of a chain recurrent set and a non-wandering set is a proper subset of the strong chain recurrent set.