Fat one-dimensional representatives of pseudo-Anosov isotopy classes with minimal periodic orbit structure

We consider isotopy classes of homeomorphisms of the disc relative to a periodic orbit. Representatives of such isotopy classes are constructed which yield piecewise linear maps of the interval on identification along stable leaves: this means that their periodic orbit structures are easily determined. In the case where the isotopy class is of pseudo-Anosov type, necessary and sufficient conditions are given for this periodic orbit structure to be minimal in the isotopy class.