Critical measures for vector energy: Global structure of trajectories of quadratic differentials KU Leuven
Saddle points of a vector logarithmic energy with a vector polynomial external field on the plane constitute the vector-valued critical measures, a notion that finds a natural motivation in several branches of analysis. We study in depth the case of measures μ =(μ1,μ2,μ3) when the mutual interaction comprises both attracting and repelling forces. For arbitrary vector polynomial external fields we establish general structural results about ...