Hamiltonian tends to $+\infty$ as $\lVert x\rVert+\lVert y\rVert\to\infty$

Question

I am a bit confused since it is said that $$ H(x,y)=\frac{y^2}{2}-\frac{x^2}{2}-\frac{x^3}{3} $$ is a global Lyapunov function and one condition for this is that $$ H(x,y)\to+\infty\text{ as }\lVert x\rVert + \lVert y\rVert\to\infty. $$ As far as I see this is not fulfilled here.