Dilatations and continued fractions
A matrix is called a primitive irreducible matrix (or in the author's terms a Perron-Frobenius matrix) if it is entrywise nonnegative and some power is entrywise positive. The author's principal result shows how to express the spectral radius and corresponding (normalized) eigenvector of a class of primitive irreducible integer matrices as generalized continued fractions. This result is applied to a problem in topology involving pseudo-Anosov maps of hyperbolic surfaces.
scientific article; zbMATH DE number 69529
scientific article