Bendixson Conditions for Differential Equations in a Banach Space

Abstract

A Bendixson Condition precludes the invariance of Jordan curves with respect to the dynamics of a differential equation $x'= f(x)$. Thus, for example, non-constant periodic orbits and homoclinic cycles are ruled out. As we know, for 2-dimensional systems if $div f$ is non-zero in a simply connected open set U in the plane, we know that there are no periodic orbits in U. We will explore such conditions in various finite and infinite dimensional spaces.

Video of the talk.