The theorems of Berkeley mathematician Marina Ratner have guided key advances in the understanding of dynamical systems. Unipotent flows are well-behaved dynamical systems, and Ratner has shown that the closure of every orbit for such a flow is of a simple algebraic or geometric form. In" Ratner's Theorems on Unipotent Flows," Dave Witte Morris provides both an elementary introduction to these theorems and an account of the proof of Ratner's measure classification theorem.
A collection of lecture notes aimed at graduate students, the first four chapters of "Ratner's Theorems on Unipotent...