Complexified dynamical systems.

Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having symmetry. The condition of symmetry selects out complex solutions that are periodic. [ABSTRACT FROM AUTHOR]