Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes

The solutions of the Henon–Heiles Hamiltonian are investigated in the complex time plane. The use of the ’’Painlevé property,’’ i.e., the property that the only movable singularities exhibited by the solution are poles, enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable. Special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes. These boundaries have a remarkable self-similar structure whose form changes as a function of the nonlinear coupling.