Let φt be a nonsingular flow on
a 3-dimensional manifold M. Denote by πP: PX → M the projectivized bundle of
the quotient bundle of TM by the line bundle tangent to φt. The derivative of φt
induces a flow ψt on PX, called the projective flow of φt. In this paper, we consider
the dynamical properties of ψt restricted to πP−1(M) for a minimal set M of φt,
under the condition that the restriction of ψt to πP−1(M) has exactly two minimal
sets N1 and N2. If φt has no dominated splitting over M, we find two types of orbits
of ψt in the domain between N1 and N2: one is “bounded below” and the
other is “bounded above”. As an application we prove that, if φt is further
assumed to be almost periodic on the minimal set, there is a dense orbit in that
domain.
