I find the following problem in Int. to Applied Nonlinear Dynamical Systems and Chaos By Stephen Wiggins (19.10 Hamiltonian Normal Forms). which say the following:
Consider two degree-of-freedom Hamiltonians near an equilibrium point where the leading order terms in the Hamiltonian are quadratic and given by $$H_{2}= \lambda p_{1}q_{1}+\frac{\omega}{2}(p_{2}^{2}+q_{2}^{2}) \hspace{3mm}\omega, \lambda>0$$ compute the normal form.
But really, I can't to use any result to find the normal form for this exercise. Could anyone give any hint?
