I'm trying to understand Sullivan's "cycles for the dynamical study..": https://www.math.stonybrook.edu/~dennis/publications/PDF/DS-pub-0033.pdf which I find very complicated being unfamiliar with the "currents" terminology.
He has a definition of a recurrence set P(F) of a foliation F: The union of the support of all foliation cycles (or invariant transverse measures), and a flow or foliation that is totally recurrent: P(F)=M
My question is if there's a simpler topological characterization of this property so that I can understand it. Suppose there'f a flow on M so that any point in M is nonwandering (for every open neighborhood there's a time when it comes back and intersects itself). Would the foliation of the flowlines be totally recurrent?
Also in general it seems there are a great many useful results in this paper, is there a relevant textbook from which I can learn the background and decipher it?
Thanks!!
