Hénon & Heiles potential: (top) (y,v) Poincaré section at (x = 0 and u > 0) and E = 1/12 for a few orbits (dotted red circles) and analytical tori (continuous dark lines) with a 12th order polynomial. (Bottom) Poincaré section at E = 1/8 for a few regular orbits (dotted red circles) and analytical tori (continuous dark lines) with an 18th order polynomial, the unplotted domain is covered by chaotic orbits.
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