  Let X be an analytic vector field defined in a neighborhood of the origin of
R^3, and let I be an analytically non-oscillatory integral pencil of X; that
is, I is a maximal family of analytically non-oscillatory trajectories of X at
the origin all sharing the same iterated tangents. We prove that if I is
interlaced, then for any trajectory T in I, the expansion of the structure
generated over the real field by T and all globally subanalytic sets is
model-complete, o-minimal and polynomially bounded.
