Chaotic extensions of dynamical systems by function algebras

Metrizable extensions of dynamical systems from function algebras

“…We will confLrm that these extensions can be troublesome in this context (see [11] or [10, Section III]). We show, however, that sources and sinks are preserved under certain conditions.…”

“…In [9] and [11], the authors introduced and studied this kind of extensions from function algebras. They say that (X, ~, 27) is a tame extension of (X, of, X) if there exists a X-invariant set E c 'tt, which generates ~t as a C*-algebra, consisting of functions having at most finitely many points of discontinuity and such that ~l contains no characteristic functions of the form 9r {~}.…”

“…The key of [9] and [11] is an alternative description of.~. Namely, .~ is the closure of the graph { (x, (f(x))f~.u): x ~ X} with respect to the product topology.…”