Nilpotent Structures in Ergodic Theory.
Nilpotent Structures in Ergodic Theory
Bernard Host and Bryna Kra
American Mathematical Society
Mathematical Surveys and Monographs; Volume 236
Host and Kra describe structures in an arbitrary measure-preserving system in order to decompose an arbitrary function into th sum of a function measurable with respect to such as a structure--a function that is orthogonal in some sense, and possibly a small-error function. They describe the structures by algebraically defined systems that are a class that includes abelian rotations, along with their natural generalizations. Such systems are nilsystems, they say: inductively constructed starting with a trivial one-point system and and ultimately capturing all of the nilpotent behavior in the system. (Ringgold, Inc., Portland, OR)