This paper continues the work of our previous papers, The cyclic spectrum of a Boolean flow TAC 10, 392-419 and Spectra of finitely generated Boolean flows TAC 16, 434-459. We define eventually cyclic Boolean flows and the eventually cyclic spectrum of a Boolean flow. We show that this spectrum, as well as the spectra defined in our earlier papers, extend to parametrized flows on Stone spaces and on compact Hausdorff space when symbolic dynamics is used. An example shows that the cyclic spectrum for a parameterized flow is sometimes over a non-spatial locale.
Keywords: Parameterized Boolean flow, dynamical systems, spectrum, sheaf
2000 MSC: 06D22, 18B99, 37B99
Theory and Applications of Categories,
Vol. 22, 2009,
No. 14, pp 345-375.