Pseudo-Anosov Maps and Invariant Train Tracks in the Disc: A Finite Algorithm

Let [f] be an isotopy class of orientation-preserving homeomorphisms of the punctured disc. We construct a finite algorithm which enables one to decide whether the class [f] contains a pseudo-Anosov element. In this case the algorithm defines an invariant train track and the dilatation factor, which gives the minimal topological entropy of the isotropy class.