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CONFLUENTES MATHEMATICI

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Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension 3
Rémi Jaoui1
1 Department of mathematics, University of Notre Dame, South Bend, Indiana
Confluentes Mathematici, Tome 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 (X,v), based on the study of rational factors of (X,v) 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
Mots clés : differentially closed fields, Anosov flows, geometric stability theory
Rémi Jaoui 1

1 Department of mathematics, University of Notre Dame, South Bend, Indiana
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Rémi Jaoui. Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension $3$. Confluentes Mathematici, Tome 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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