Submission date: 22 March 2018

Abstract:

In this article, we prove that, under some suitable assumptions, the generic type of a real absolutely irreducible D-variety of dimension 3 with a mixing Anosov real-analytic flow satisfies exactly one of the two following behaviors: either it is minimal and disintegrated, or it is interalgebraic over ℝ with the third power of the generic type of a disintegrated D-curve.
For that matter, we prove a conjecture of my thesis on the algebraic dynamical properties of an algebraically presented mixing Anosov flow - namely that, under the same suitable assumptions, a D-variety of dimension 3 with a mixing Anosov real-analytic flow does not admit non-trivial rational factors.
Then, the first statement follows from the second - using the Trichotomy Theorem in the theory DCF_0 - and the property of orthogonality to the constants for the aforementionned D-varieties.

Mathematics Subject Classification: 03C95, 12H05, 37D20

Keywords and phrases:

Full text arXiv 1803.08811: pdf, ps.