Geometry of Reflecting Rays and Inverse Spectral Problems

The behaviour of reflecting rays plays an essential role in many problems of mathematical physics. This book studies different geometric properties of reflecting rays for manifolds with smooth boundary and their applications to different inverse spectral and scattering problems. This is a developing area in which the authors have made important contributions. Results concerning the particular problems studied and which arise in several important domains of modern physics are presented. Some chapters concerning the generic properties of reflecting rays can be used for courses for graduate students.

The behavior of reflecting rays plays an essential role in many problems of mathematical physics. Various geometric properties of these rays for manifolds with smooth boundary are studied and their applications to different inverse spectral and scattering problems are discussed. Distinguishing features include coverage of manifolds of jets and spaces of smooth maps and transversity, an in-depth study of inverse spectral problems for the Laplacian in generic bounded domains, and discussion of the singularities of the scattering kernel and solving the problem of its description.