Model Theory Seminar | Yutong Duan | Strong minimality of Lotka-Volterra system

We will begin with the notion of irreducibility for differential equations, introduced by Painlevé in his search for new transcendental functions, and explain its relationship with strong minimality. We will then introduce the Lotka–Volterra system and try to show that, under certain conditions on the parameters, its degree of non-minimality is zero; by convention, this means that its generic type is minimal. Finally, we will show that the resulting strongly minimal set has trivial geometry; moreover, it is strictly disintegrated.

MC 5403