On the density of strongly minimal algebraic vector fields
Abstract : Two theorems witnessing the abundance of geometrically trivial strongly minimal autonomous differential equations of arbitrary order are shown....
Abstract : Two theorems witnessing the abundance of geometrically trivial strongly minimal autonomous differential equations of arbitrary order are shown....
Abstract: We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collaps...
An electronic circuit described by an equation of Liénard. Abstract: We study the structure of the solution sets in universal differential field...
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...
Abstract : Several results on the birational geometry of algebraic vector fields in characteristic zero are obtained. In particular, (1) it is shown that...
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...
Representation of a complex hyberbolic singularity. Abstract: In this article, we study model-theoretic properties of algebraic differential equa...
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...
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...
Abstract: This thesis is dedicated to studying the interactions between two different approaches regarding differential equations: the model-theory of differ...