Topologically Transitive Continuous Semi-flow Chaos And Topological Strong Mixing,

In this paper,we study the complexity of transitive continuous semi-flow on compact metric space.The first result is that the transitive continuous semi-flow with a periodic point is Li-Yorke chaotic.It follows that Devaney's chaos implies Li-Yorke's chaos.Second,we prove that the topological transitive C~1-flow with a fixed point on compact closed surface is topological strong mixing.