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 \( E \).


Simulation

\(E = \) You must enter a decimal number between $0.05$ and $0.15$.

Poincaré map of the Hénon-Heiles model


Bibliography

H. Dang-Vu and C. Delcarte. Bifurcations et chaos: une introduction à la dynamique contemporaine avec des programmes en Pascal, Fortran et Mathematica. Universités. Mécanique. Ellipses, 2000.

L. Perko. Differential equations and dynamical systems. Springer, New York, 3rd edition, 2001.