Generating quadratic pseudo-Anosov homeomorphisms of closed surfaces (Q1397902)

A homeomorphism \(f\) of a compact surface is called pseudo-Anosov if its isotopy class contains a homeomorphism \(g\) with the following properties: \(g\) leaves invariant a pair of transverse measurable foliations \(F^u\) and \(F^s\), and there exists a number \(\lambda>1\) such that \(g(F^u)=\lambda F^u\) and \(g(F^s)=\mu F^s\), where \(\lambda\mu=1\). The author shows that for any closed orientable surface \(S\), any hyperbolic toral automorphism has a positive power which induces a pseudo-Anosov homeomorphism \(f\) of \(S\) such that the corresponding foliation is orientable and \(\lambda\) is a quadratic integer.