Eventually expansive semiflows

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<p style='text-indent:20px;'>A semiflow is <i>eventually expansive</i> if there is a prefixed radius up to which two orbits eventually coincide. We prove the following result: Every injective eventually expansive semiflow of a compact metric space consists of finitely many closed orbits and, in the noncompact case, the semiflow cannot have global attractors. The suspension of a continuous map is eventually expansive only if the map is positively expansive. The suspension of every positively expansive map is an eventually expansive semiflow. The topological entropy of an eventually expansive semiflow is bounded from below by the growth rate of the periodic orbits. We present some related examples.</p>