Dehn twists and pseudo-Anosov diffeomorphisms
The author shows that it is possible to obtain many pseudo-Anosov diffeomorphisms from Dehn twists. Let M be a closed and oriented surface. The set of isotopy classes of simply connected closed curves on M is denoted by \({\mathcal S}(M)\), the set of isotopy classes of diffeomorphisms by \(\pi_ 0(Diff(M))\). He proves the following theorem: Let f be in \(\pi_ 0(Diff(M))\) and let \(\gamma\) be in \({\mathcal S}(M)\). If the orbit of \(\gamma\) under f fills M, then \(T^ n_{\gamma} f\) is a pseudo-Anosov class except for at most 7 consecutive values of n.
scientific article; zbMATH DE number 4003112
scientific article