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-E, N); x := `mod`(z+z+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!