The logistic map with parameter $r=4$ and the tent map with parameter $\mu=2$ are topologically conjugate chaotic dynamical systems.
Question
Given an infinite set of points $S$ within the domain, how does one show that the map acts transitively upon the set?
What do I mean by "acts transitively"? I don't intend to redefine any terms here but I'm interested in general how one would determine whether that set is contained within the preimage of some periodic orbit. I'm aware some sets will converge upon a common trajectory which may not be periodic, and the map is also considered transitive over those.
A reference or references would be fine.