1D betatron resonance in phase space

SetOptions[{Plot,ParametricPlot,ListPlot,ContourPlot},AspectRatio->1,LabelStyle->{FontFamily->"Times New Roman",24},PlotRange->{{-2,2},{-2,2}},ImageSize->{600,600}];

Starts at m=n=tune=1

Manipulate[sols=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}];
ParametricPlot[{Evaluate[{x[θ],x'[θ]/ν}/.sols]},{θ,0,2 π T},PlotPoints->600,AxesLabel->{"x","x'/ν"}],{{p,{0.,1.}},Locator},{{T,32,"turns"},.01,100,.01},{{n,1,"order (n)"},1,3,1},{{m,1,"harm (m)"},1,3,1},{{ν,1.,"tune (Subscript[ν, x])"},0,2,.01},
{{a0,.0144,"strength (a0)"},-0,.05,.01},AppearanceElements->All]