On a vector equilibrium problem

We will talk on a vector equilibrium problem for the logarithmic potentials with Angelesco type of matrix of interaction. The problem arose in a natural way during the description of the limit distribution of the zeros of polynomials mutually orthogonal on disjoint segments. We consider a class of charge solutions to the problem and also a class of measure solutions for the case of two arbitrary segments. We consider the relation of the solutions to the problem with algebraic functions and also discuss some of properties of these solutions.