TOPOLOGICAL ENTROPY OF EXPANSIVE FLOW ON TVS-CONE METRIC SPACES

We shall study the following. Let phi be an expansive flow on a compact TVS-cone metric space (X,d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that limsup {1over t} log v(t) le h(phi), where v(t) denotes the number of closed orbits of phi with a period tau in [0,t] and h(phi) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space