  We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices
with rational symbol as the size of the matrix goes to infinity. Our main
result is that the weak limit of the normalized eigenvalue counting measure is
a particular component of the unique solution to a vector equilibrium problem.
Moreover, we show that the other components describe the limiting behavior of
certain generalized eigenvalues. In this way, we generalize the recent results
of Duits and Kuijlaars for banded Toeplitz matrices.

Complex Variables;Classical Analysis and ODEs