Extension of flows via discontinuous functions (Q1113129)

A classical construction in topological dynamics is to take an irrational rotation of the unit circle and form a new flow by ``cutting up'' an orbit. This is equivalent to taking a characteristic function, and creating the smallest space on which it and its translates are continuous. The authors look at this situation more generally for arbitrary flows (X,T), where X is compact \(T_ 2\), T is a topological group, and certain (discontinuous) functions f: \(X\to W\), where W is compact \(T_ 2\), using a ring extension approach. General dynamical properties of the model as developed, and questions about isomorphism and classes of function are considered. Finally, it is shown that when t is locally compact \(T_ 2\), every minimal almost 1-1 extension of (X,T) is obtained in this fashion.