On computing Poincaré map by Hénon method

The trajectory of the autonomous chaotic system deviates from the original path leading to a deformation in its attractor while calculating Poincaré map using the method presented by Hénon [Hénon M. Physica D 1982;5:412]. Also, the Poincaré map obtained is found to be the Poincaré map of deformed attractor instead of the original attractor. In order to overcome these drawbacks, this method is slightly modified by introducing an important change in the existing algorithm. Then it is shown that the modified Hénon method calculates the Poincaré map of the original attractor and it does not affect the system dynamics (attractor). The modified method is illustrated by means of the Lorenz and Chua systems.