Abstract

L. Markus noticed in 1960 that one can associate to a homogeneous quadratic ordinary differential equation a commutative, not necessarily associative algebra, in a procedure quite similar to associating a linear map to a linear differential equation. Thus one establishes a correspondence between a class of differential equations and a class of algebraic structures, and hope to use algebraic techniques for the investigation of differential equations. Success is far from guaranteed for this approach, as should be expected: The class of quadratic differential equations is simply too large and versatile to allow strong universal results. But there are some useful general notions and results, and there are particular classes of equations which are quite amenable to an approach via nonassociative algebras.
The material presented in this talk will be the background for the seminar entitled "Rotation sets for graph maps of degree 1" (March 14, 2005).