Mike Field (University of Houston) Title: Not so trivial, trivial dynamics. Abstract: We describe some recent work on product dynamics involving homoclinic and heteroclinic cycles that arose out of earlier work (with Peter Ashwin, Exeter) on products of homoclinic cycles that involved some surprisingly subtle connections with analytic number theory. The work we describe is joint with Alexandre Rodrigues (Porto) and Nikita Agarwal (University of Houston).