A real number gives rise to a Sturmian system encoding a rotation of the circle, and there are several beautiful connections between these systems and arithmetic properties of the associated parameters. One is a result of Fokkink, which shows that two Sturmian subshifts with parameters \alpha and \beta are flow equivalent if and only if \alpha and \beta lie in the same orbit of the action of PSL_2(Z) on the set of reals via Mobius transformations, a condition which is itself characterized by the tails of their continued fraction expansions. I’ll describe some recent work, joint Christopher-Lloyd Simon, describing the action of PSL_2(Q) in terms of a certain relation on systems called isogeny.