I am consider the following Hamiltonian: $$\mathcal{H} = \frac{1}{2}(\dot{x}^2 + \dot{y}^2) + \frac{1}{2}(x^2 + y^2) + x^2y - \frac{y^3}{3}.$$ The first step I took were to solve the equations of motion which gave me 4 functions: $x(t)$, $\dot{x}(t)$, $y(t)$, $\dot{y}(t)$. However in the Wikipedia article on Lyapunov Exponents, their equation for the maximal Lyapunov exponent $$\lambda(x_0) = \lim_{n\to0}\frac{1}{n}\sum_{i=0}^{n-1}\ln{|f'(x_i)|}$$ depends only on one function $f(x)$. How does this generalize to my system?
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