The volume is dedicated to Professor Robert Ellis for his pioneering work and
influence in the development of the abstract theory of Topological Dynamics.
grew out of a conference in honor of his retirement, held on April 5 and 6, 1995 at
the University of Minnesota.
Prof. Robert Ellis in his life long work laid the foundation for an algebraic
approach to topological dynamics. With the introduction of the notion of an en-
veloping semigroup R. Ellis began demonstrating how to capture the asymptotics of
a dynamical system in terms of the algebraic features of a suitable compactification
of the acting group. This work highlights the intrinsic interplay between algebra and
analysis. Over the next twenty-five years Professor Ellis single handedly developed
this theory, culminating in what is now known as the "Galois theory of minimal
flows". During this period he proved deep structure theorems about dynamics of
group actions which in turn gave a finer understanding of the equicontinuous and
distal structure relations. This work provides ample evidence for his belief that
topological dynamics is worthy of study as a discipline unto itself.
In addition to the abstract structure theory, R. Ellis's contributions to mathe-
matics include papers encompassing other areas of mathematics like ergodic theory,
theory of random walks and boundary theory of locally compact groups, actions of
semi simple groups, combinatorial number theory and differential equations. This
volume is divided into three parts in recognition of Ellis's influence on other math-
ematicians and other branches of mathematics.
Finally this preface would never be complete without mentioning his influence
as a teacher on many of us. His unique style, enduring support and constant
encouragement is experienced and cherished by many. We take this opportunity to
express our respect, gratitude and love.
The Editors wish to thank Prof. Yingfei Yi for his editorial contribution, the
excellent editorial staff at the A.M.S., in particular Ms. Donna Harmon and Ms.
Christine M. Thivierge for their patience, advice and guidance.