Poincaré map
The following application computes a Poincaré map of the Hénon-Heiles model, given by the hamiltonian
\begin{equation*}
H = \dfrac{1}{2} \left(p_x^2 + p_y^2 + x^2 + y^2 \right) + x^2 y - \dfrac{1}{3} y^3 ,
\end{equation*}
using the Hénon trick
[DangVu and Delcarte (2000),
Perko (2001)].
As proved with the KAM theory, an increase of the energy \( E \) destroys the tori.
You just have to enter a decimal value between
\( 0.05 \) and \( 0.15 \)
for the energy parameter \( E \).
