Two-parameter families of strange attractors.

Periodically driven two-dimensional nonlinear oscillators can generate strange attractors that are periodic. These attractors are mapped in a locally 1-1 way to entire families of strange attractors that are indexed by a pair of relatively prime integers (n(1),n(2)), with n(1)>/=1. The integers are introduced by imposing periodic boundary conditions on the entire strange attractor rather than individual trajectories in the attractor. The torsion and energy integrals for members of this two parameter family of locally identical strange attractors depend smoothly on these integers.