Semiclassical theory of short periodic orbits in quantum chaos

We have developed a semiclassical theory of short 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 N po ≃ T H , with T H the Heisenberg time. As a result N po ≃ hT H / ln ( hT H ), where h is the topological entropy. For methods related to the trace formula N po ≃ exp ( hT H ) / ( hT H ).