Abstract:

Important aspects of ray chaos will be reviewed, emphasizing topics which relate to the Hamiltonian structure of the ray equations. Topics to be discussed include integrable and nonintegrable ray systems, action-angle variables, the breakdown of canonical perturbation theory, the KAM theorem, area-preserving mappings, power spectra, Lyapunov exponents, and the notion of a ``predictability horizon.'' Connections between ray chaos and chaos in the classical limit of quantum mechanics will be discussed. The notion of ``wave chaos'' will be introduced. The important, and as yet unresolved, question of whether ray-based wavefield representations break down under chaotic conditions at a range which is proportional to the logarithm of the acoustic frequency will be discussed. [Work supported by ONR.]