Focusing on the role that automorphisms and equivalence relations
play in the algebraic theory of minimal sets provides an original
treatment of some key aspects of abstract topological dynamics.
Such an approach is presented in this lucid and self-contained
book, leading to simpler proofs of classical results, as well as
providing motivation for further study. Minimal flows on compact
Hausdorff spaces are studied as icers on the universal minimal flow
M. The group of the icer representing a minimal flow is defined as
a subgroup of the automorphism group G of M, and icers are
constructed explicitly as relative products using subgroups of G.
Many classical results are then obtained by examining the structure
of the icers on M, including a proof of the Furstenberg structure
theorem for distal extensions. This book is designed as both a
guide for graduate students, and a source of interesting new ideas
for researchers.
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