Expanding factors for pseudo-Anosov homeomorphisms
Let \(f : M \rightarrow M\) be a pseudo-Anosov homeomorphism on an orientable surface of genus \(g\) with oriented unstable manifolds. Let \(\mathcal P\) be a Markov partition for \(f\) with Markov matrix \(A\). If \(f\) preserves the orientation of unstable manifolds, then the eigenvalues of \(f_{*1} : H_1(M,R) \rightarrow H_1(M,R)\) are the same as those of \(A\) including multiplicity, with the possible exception of some zeros and roots of unity.
scientific article; zbMATH DE number 1548315