Question: How to plot in maple?

Hello,

I am trying to plot this map

y:=y[t+1] +e(x[t]) mod N
x:=x[t]+y[t+1] mod N

where e(x[t]) is a piecewise function defined by

e(x[t])=1 if 0<=x< floor(N/2) OR

e(x[t])=-1 if floor(N/2) <=x<N
for any initial conditions [x,y] and N (but must be integers).
What I did is two separate functions: 1) for e(x[t]) functiion is given by

E := proc (x, N) global e; if 0 <= x and x <= floor((1/2)*N) then e := 1 else e := -1 end if end proc

and 2) for the main function

S := proc (z) local i, x, y, c, e; global N, E; y := `mod`(z[2]-E, N); x := `mod`(z[1]+z[2]+E, N); return [x, y] end proc

My orbit procedure (so that the output is list of integers [x,y]) is given by:

This DataPlot does not give the list output of integers. I do not know whether this function is correctly written. 
Can somebody help me producing the list of the orbit [x,y]?
Thank you very much for helping!