Let say I have this equation,
Yt+1=Yt +sign(Xt)
Xt+1=Xt+a(Yt+1)+b where a,b are integers and 0 < b < a.
If gcd(a,b)=d, then how can I find the sublattice by looking at the coordinates? This is really confusing.
Let say I choose any point [x,y]= [50,10], depending on the gcd(a,b), the coordinates change. I need to find the conjugacy equation that can simplify the case of gcd(a,b)=d to gcd(a/d,b/d)=1 which makes me really confusing!