1D betatron resonance in phase space, but strobed so trajectories

Off[InterpolatingFunction::dmval];Manipulate[sol=NDSolve[{x''[θ]+(ν^2) x[θ]==a0 ((x[θ])^(n-1)) Cos[m θ],x[0]==p[[1]],x'[0]==ν p[[2]]},x,{θ,0,2 π T},AccuracyGoal->12];
ListPlot[Table[Evaluate[{x[2 π np/m],x'[2 π np/m]/ν}/.sol],{np,0,T m}],AxesLabel->{"x","x'/ν"},PlotStyle->Red],{{p,{1.2908,.0}},Locator},{{T,100,"turns"},1,200,1},{{n,3,"order (n)"},1,4,1},{{m,1,"harm (m)"},1,4,1},{{ν,0.34,"tune (Subscript[ν, x])"},0,2,.01},
{{a0,.0144,"strength (a0)"},-.0,.05,.001},AppearanceElements->All]