Chaos in a topologically transitive semi-flow

In this paper, we study the chaotic phenomena in a topologically transitive, continuous semi-flow, and show that the erratic time dependence of orbits in such a semiflow is more complicated than the one described by LiYorke chaos. Also, we generalize the notion of sensitive dependence on initial conditions for semi-flows and explore the chaotic phenomena for topologically transitive, continuous semi-flows with the generalized sensitivity property. Our results extend the existing results to semi-flows.