Topological entropy of one-dimensional Williams solenoids

In the present paper, we make correspond to each extending mapping of a ramified one-dimensional manifold into itself, which satisfies the natural conditions, an integer-valued matrix with nonnegative elements. It is proven that the topological entropy of this mapping, and the shift automorphism generated by it of the corresponding Williams solenoid, equals the logarithm of the maximal eigenvalue of the matrix thus introduced.