Collision and escape orbits in a generalized Hénon–Heiles model

摘要: Abstract The motion of a material point unit mass in field determined by generalized Henon–Heiles potential U = A q 1 2 + B C D 3 , with ( ) standard Cartesian coordinates and ∈ 0 ∞ × R is addressed for two limit situations: collision escape. Using McGehee-type transformations, the corresponding infinity boundary manifolds pasted on phase space are determined. These fictitious manifolds, but, due to continuity respect initial data, their flow determines near orbit behaviour. dynamics fully described. topology manifold independent parameters. In full space, while spiraling orbits present, most avoid collision. changes as ratio between varies. More precisely, there symmetric pitchfork bifurcations along line − reshaping bifurcation line. Besides rectilinear orbits, near-escape includes oscillatory which angular momentum alternates sign.