# Max dimensions of phase space

1. Aug 2, 2009

### coolnessitself

I'm working on a visualizer of sorts for a system:
$$x_{n+1} = sin(a y_n) - cos(b x_n)$$
$$y_{n+1} = sin(c x_n) - cos(d y_n)$$
with $$a,b,c,d \in [-2.5, 2.5]$$
So for whatever initial $$(x_0,y_0)$$ I give the system, I know the next iteration will have both x and y between -2 and 2, and that will be true for all n>0.
However, for certain values of a,b,c,d, you could say that all $$x_{n>0}$$ and $$y_{n>0}$$ will be within some other, possibly smaller, area. How can I find these dimensions given a,b,c,d?

(I'll use this to scale the area on which the plot is drawn, so for those values of a,b,c,d which result in a small area, the plot will fill the entire space)

2. Aug 7, 2009