CONFLUENTES MATHEMATICI

Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension $3$
Confluentes Mathematici, Volume 12 (2020) no. 2, pp. 49-78.

In this article, we develop a geometric framework to study the notion of semi-minimality for the generic type of a smooth autonomous differential equation $\left(X,v\right)$, based on the study of rational factors of $\left(X,v\right)$ and of algebraic foliations on $X$, invariant under the Lie derivative of the vector field $v$.

We then illustrate the effectiveness of these methods by showing that certain autonomous algebraic differential equation of order three defined over the field of real numbers — more precisely, those associated to mixing, compact, Anosov flows of dimension three — are generically disintegrated.

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DOI: 10.5802/cml.68
Classification: 03C60,  12H05
Keywords: differentially closed fields, Anosov flows, geometric stability theory
Rémi Jaoui 1

1 Department of mathematics, University of Notre Dame, South Bend, Indiana
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Rémi Jaoui. Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension $3$. Confluentes Mathematici, Volume 12 (2020) no. 2, pp. 49-78. doi : 10.5802/cml.68. https://cml.centre-mersenne.org/articles/10.5802/cml.68/

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