Analytic structure and integrability of dynamical systems

The solutions to the equations of motion of certain dynamical systems are investigated as a function of complex time. The use of the “Painlevé property,” i.e., the property that the only movable singularities exhibited by the solution are poles, enables a prediction of system parameter values for which the system is integrable. The method is illustrated by a study of the Henon‐Heiles system. Extension of the analysis to movable branch points reveals at least one more integrable case. Further changes in analytic structure correlate with the onset of widespread chaos.