  We study the properties of orthogonality to the constants and disintegration
for autonomous algebraic differential equations. We present a criterion of
orthogonality to the constants for absolutely irreducible real $D$-varieties
relying on the topological dynamic of the associated real analytic flow. More
precisely, we prove that if there exists Zariski-dense invariant compact region
of the smooth locus of real points of $X$ where the dynamic of the real
analytic flow is topologically weakly mixing, then the generic type of $(X,v)$
is orthogonal to the constants. This criterion will be applied in a second part
of this article to establish some transcendance properties for the geodesics of
a compact algebraically presented compact Riemannian manifold with negative
curvature.
