Abstract
We have developed a semiclassical theory of short periodic orbits to obtain all the quantum information of a bounded chaotic Hamiltonian system. If T1 is the period of the shortest periodic orbit, T2 the period of the next one and so on, the number Npo of periodic orbits required in the calculation is such that T1 + + TNpo TH, with TH the Heisenberg time. As a result Npo hTH / ln (hTH), where h is the topological entropy. For methods related to the trace formula Npo exp (hTH) / (hTH).
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