# Posts by Year

## 2022

### Abelian reduction in differential-algebraic and bimeromorphic geometry

Abstract : Several results on the birational geometry of algebraic vector fields in characteristic zero are obtained. In particular, (1) it is shown that...

### When any three solutions are independent

Abstract: Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any numb...

### The degree of nonminimality is at most two

Abstract : It is shown that if $$p$$ is a complete type of Lascar rank at least 2 over $$A$$, in the theory of differentially closed fields of charact...

### On the equations of Poizat and Liénard

An electronic circuit described by an equation of Liénard. Abstract: We study the structure of the solution sets in universal differential field...

## 2021

### Generic planar algebraic vector fields are strongly minimal and disintegrated

Representation of a complex hyberbolic singularity. Abstract: In this article, we study model-theoretic properties of algebraic differential equa...

### Relative internality and definable fibrations

Abstract: We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collaps...

### Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension 3

An Anosov flow of dimension three. Abstract: In this article, we develop a geometric framework to study the notion of semi-minimality for the gen...

### Corps différentiels et flots géodésiques I: Orthogonalité aux constantes pour les équations différentielles autonomes

A weakly-mixing discrete dynamical system. Abstract: Orthogonality to the constants is property of an algebraic differential equation that origin...

Abstract: We define the notion of a smooth pseudo-Riemannian algebraic variety $$(X,g)$$ over a field $$k$$ of characteristic 0, which is an algebraic an...