Classical invariants and the quantum-classical link

The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic systems. Based on trace formulae, we construct smooth functions highly localized in the neighborhood of periodic orbits using only quantum information. Those functions show how classical hyperbolic structures emerge from quantum mechanics in chaotic systems. Finally, we discuss the proper quantum-classical link.