We study the relationship between classical and quantum structures for a map on the sphere whose behavior can be chaotic in the classical limit. On the classical side we implement an efficient method to locate periodic points on symmetry lines. On the quantum side we show how matrix elements of the propagator in the coherent-state representation are connected to classical structures. Diagonal and off-diagonal matrix elements are related to periodic points, symmetry lines, and other invariant structures in phase space, both in the time and in the energy domains. The scarring phenomena related to the short periodic orbits and their homoclinic neighborhoods are discussed.

• Received 1 August 1991

DOI:https://doi.org/10.1103/PhysRevA.45.3646