Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists of enriching a plane field, as this is often practised in control theory, by adding brackets of the vector fields tangent to it and, then, looking for singular solutions of the obtained distribution. We apply this to the isometry problem of rigid geometric structures.

These two books look like they might form a two-volume set, but this is not so. The first is an introduction to ergodic theory suitable as a text for a first course in the subject, with some of the standard results viewed in an unusual light (that of descriptive set theory) and with detailed discussion of several topics of special interest to the author. The second is a survey at an advanced level of parts of the interaction of measure-preserving and nonsingular ergodic theory with spectral theory and harmonic analysis. It assumes considerable background in all three of these subjects and is written as a guide for researchers, organizing many topics of recent and current interest and highlighting some major open questions on which further progress might be possible at this time. Selected topics could be worked through individually or as part of a seminar or advanced course. Interestingly, the second does not even refer to the first for needed results from basic ergodic theory.