Submission date: 19 December 2016

Abstract:

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 the model-theoretic study of the geodesic flow of compact real algebraic Riemannian manifolds with negative curvature.

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Full text arXiv 1612.06222: pdf, ps.