Orthogonality to the constants is property of an algebraic differential equation that originated from the model-theoretic study of differential fields and  that expresses remarkable independence properties for its solutions

In this article, we study the property of orthogonality to the constants in a differential algebraic language for autonomous differential equations and describe some effective methods to establish this property. The main result is a criterion for orthogonality to the constants (and its version for families) for real absolutely irrecucible $D$-varieties $(X,v)$ based on the dynamical properties of the associated real analytic flow  $(M,\phi)$.  More precisely, we show that if there exists  a compact region $K$ of $M$, Zariski-dense in $X$ and such that the restriction of the flow $\phi$ to $K$ is topologically weakly mixing  then the generic type of $(X,v)$ is orthogonal to the constants.

This criterion will be applied in [18] to study from this model-theoretic point of view the geodesic flow of a compact Riemannian varieties (presented algebraically) with negative curvature.