Consider the variant of the standard map described by the recursion relation

\[y_{n+1}=y_{n}+k \sin x_{n} \quad, x_{n+1}=x_{n}+y_{n+1}\]

where \(k\) is a constant.

(a) Study the distortion of the KAM tori as \(k\) is taken from \(k=0\) to \(k=0.6\).

(b) Analyze the system when \(k=0.9716\). Compute the 'winding number' \(\Omega \equiv \lim _{n \rightarrow \infty}\left(x_{n}-x_{1}\right) / n\) as a function of \(k\).