  Differentially positive systems are the nonlinear systems whose linearization
along trajectories preserves a cone field on a smooth Riemannian manifold. One
of the embryonic forms for cone fields in reality is originated from the
general relativity. By utilizing the Perron-Frobenius vector fields and the
$\Gamma$-invariance of cone fields, we show that generic (i.e.,``almost all" in
the topological sense) orbits are convergent to certain single equilibrium.
This solved a reduced version of Forni-Sepulchre's conjecture in 2016 for
globally orderable manifolds.
