This paper defines flows (or discrete dynamical systems) and cyclic flows in a category and investigates how the trajectories of a point might approach a cycle. The paper considers cyclic flows in the categories of Sets and of Boolean algebras and their duals and characterizes the Stone representation of a cyclic flow in Boolean algebras. A cyclic spectrum is constructed for Boolean flows. Examples include attractive fixpoints, repulsive fixpoints, strange attractors and the logistic equation.
Theory and Applications of Categories, Vol. 10, 2002, No. 15, pp 392-409 http://www.tac.mta.ca/tac/volumes/10/15/10-15.dvi http://www.tac.mta.ca/tac/volumes/10/15/10-15.ps http://www.tac.mta.ca/tac/volumes/10/15/10-15.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/15/10-15.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/15/10-15.psTAC Home