I have been studying the 2D Henon Map and I am trying to approximate the last KAM manifold. In order to do that, I am using a mathematical tool called rotational number.For this problem I am trying to create a sequence of rotational numbers of manifolds which converge to the rotational number for the manifold I am looking for. Until now I have found that number to be given by this continued fraction
$x=[0,5,2,1,2,1,2]$
I can see that this will probably be a periodic number and I am also aware that I can find a correspoding quadratic expression for this number to help me acquire it in a closed form. But I am not sure how to do so. The part of $[1,2,1,2]$ repeats but $5$ appears only once.
How shoud I proceed? Thank you.