  In this paper, we present a new method via the transfer matrix approach to
obtain asymptotic formulae of orthogonal polynomials with asymptotically
identical coefficients of bounded variation. We make use of the hyperbolicity
of the recurrence matrices and employ Kooman's Theorem to diagonalize them
simultaneously. The method introduced in this paper allows one to consider
products of matrices such that entries of consecutive matrices are of bounded
variation.
  Finally, we apply the asymptotic formulae obtained to solve the point mass
problem on the real line when the measure is essentially supported on an
interval. We prove that if a point mass is added to such a measure outside its
essential support, then the perturbed recurrence coefficients will also be
asymptotically identical with the same limit and of bounded variation.
