In my opinion another interesting reference is "An algebraic approach to chaos""An algebraic approach to chaos" (Appl. Cat. Struct. 4 (1996) 423-441) by Susan Niefield. Unfortunately I could find neither a free version nor any followup anywhere, which is a pity. She had very interesting approach to formulating phenomena related to ergodicity and some of its topological analogs like topological transitivitytopological transitivity in a localic way which permitted her to treat metric, topological and algebraic cases in parallel.