Equations Admitting Scaling and Discrete Cyclic Symmetries

Some coordinate transformations on two variables are obtained that give a realization of the cyclic group. The differential invariants of scaling transformations are then combined to give quantities that are multiplied by a complex root of unity when the cyclic transformations are applied. The second order ordinary differential equations that are invariant under both scaling and the cyclic transformations can then be written down. Q 1996 Academic Press, Inc.