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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Keywords: differentially closed fields, Anosov flows, geometric stability theory

Rémi Jaoui ^{1}

@article{CML_2020__12_2_49_0, author = {R\'emi Jaoui}, title = {Rational factors, invariant foliations and algebraic disintegration of compact mixing {Anosov} flows of dimension $3$}, journal = {Confluentes Mathematici}, pages = {49--78}, publisher = {Institut Camille Jordan}, volume = {12}, number = {2}, year = {2020}, doi = {10.5802/cml.68}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.68/} }

TY - JOUR AU - Rémi Jaoui TI - Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension $3$ JO - Confluentes Mathematici PY - 2020 SP - 49 EP - 78 VL - 12 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.68/ DO - 10.5802/cml.68 LA - en ID - CML_2020__12_2_49_0 ER -

%0 Journal Article %A Rémi Jaoui %T Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension $3$ %J Confluentes Mathematici %D 2020 %P 49-78 %V 12 %N 2 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.68/ %R 10.5802/cml.68 %G en %F CML_2020__12_2_49_0

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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