Semiclassical theory of short periodic orbits in quantum chaos

We have developed a semiclassical theory of shea periodic orbits to obtain all the quantum information of a bounded chaotic Hamiltonian system. If T-1 is the period of the shortest periodic orbit, T-2 the period of the next one and so on, the number N-po of periodic orbits required in the calculation is such that T-1 +...+ T-Npo similar or equal to T-H, with T-H the Heisenberg time. As a result N-po similar or equal to hT(H)/ ln(hT(H)), where h is the topological entropy. For methods related to the trace formula N-po similar or equal to exp(hT(H))/(hT(H)).