Consider the two dimensional recursion [x_{n+1}=y_{n}+1-alpha x_{n}^{2} quad, quad y_{n+1}=beta x_{n},] introduced by Hnon to describe chaotic behavior in the trajectories of asteroids. Study the

Consider the two dimensional recursion

\[x_{n+1}=y_{n}+1-\alpha x_{n}^{2} \quad, \quad y_{n+1}=\beta x_{n},\]

introduced by Hénon to describe chaotic behavior in the trajectories of asteroids. Study the sequence for \(\alpha=1.4\) and \(\beta=0.3\) with the initial condition \(x_{0}=0.63135448\) and \(y_{0}=0.18940634\). Explore the parameter space for interesting features.