  The automorphisms of a two-generator free group acting on the space of
orientation-preserving isometric actions of on hyperbolic 3-space defines a
dynamical system. Those actions which preserve a hyperbolic plane but not an
orientation on that plane is an invariant subsystem, which reduces to an action
on R^3 by polynomial automorphisms preserving the cubic polynomial and an area
form on the level surfaces.
  We describe the dynamical decomposition of this action. The domain of
discontinuity of this action corresponds to geometric structures: either
complete hyperbolic structures on the 2-holed cross-surface (projective plane)
with cusps and funnels, or complete hyperbolic structures on a one-holed Klein
bottle, or hyperbolic structures on a Klein bottle with one conical
singularity. The action is ergodic on the complement of the orbit of the Fricke
space of the 2-holed cross-surface, and we show that the orbit of the
generalized Fricke space of the one-holed Klein bottle is open and dense.
