Approximate first integrals of the Hénon-Heiles system revisited

Approximate first integrals (conserved quantities) of Hénon-Heiles system have been obtained based on the approximate Noether symmetries for the resonance (ω2=ω1) and off resonance. It has been shown that system undergoes complicated bifurcations near resonances. Analytical results have been verified by numerically obtained KAM curves on the Poincaré surface of section.