Chaos in dynamical systems by the Poincaré-Melnikov-Arnold method

Marsden, J. E.

Chaos in Nonlinear Dynamical Systems, SIAM, (J. Chandra, ed.), (1984), 19-31


Methods proving the existence of chaos in the sense of Poincaré-Birkhoff-Smale horseshoes are presented. We shall concentrate on explicitly verifiable results that apply to specific examples such as the ordinary differential equations for a forced pendulum, and for superfluid He and the partial differential equation describing the oscillations off a beam. Some discussion of the difficulties the method encounters near an elliptic fixed point is given.