formula_33 is a phase that depends on the Maslov index and other details of the orbits. formula_34 is the recurrence amplitude of a closed orbit for a given initial state (labeled formula_35). It contains information about the stability of the orbit, its initial and final directions, and the matrix element of the dipole operator between the initial state and a zero-energy Coulomb wave. For scaling systems such as Rydberg atoms in strong fields, the Fourier transform of an oscillator strength spectrum computed at fixed formula_5 as a function of formula_37 is called a recurrence spectrum, because it gives peaks which correspond to the scaled action of closed orbits and whose heights correspond to formula_34.