Consider the recursion relation [x_{n+1}=x_{n}+y_{n} quad, quad y_{n+1}=a y_{n}-b cos left(x_{n}+y_{n} ight)] where (a) and (b) are

Consider the recursion relation

\[x_{n+1}=x_{n}+y_{n} \quad, \quad y_{n+1}=a y_{n}-b \cos \left(x_{n}+y_{n}\right)\]

where \(a\) and \(b\) are constants; this system is known as the standard map. Analyze the system as we did for the logistic map in the text. In particular, explore regions of the parameter space where (1) \(a=1\) and (2) \(a=1 / 2\) while varying \(b\), (3) \(b=6\) near point (3,3).