Abstract
The motion of a material point of unit mass in a field determined by a generalized Hénon‐Heiles potential U = Aq12+Bq22+Cq12q2+Dq23, with (q1,q2) = standard standard Cartesian coordinates and (A,B,C,D)∈(0,∞)2×R2, is addressed in the escape limit situation. Using McGehee‐type transformations, the corresponding infinity boundary manifold pasted on the phase space are determined. This is fictitious, but, due to the continuity with respect to initial data, its flow determines the near by orbit behaviour. The topology of the flow on the infinity manifold changes as the ratio between C and D varies. More precisely, there are two symmetric pitchfork bifurcations along the line 2C−3D = 0, due to the reshaping of the potential along the bifurcation line.
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