  This survey gives a unified treatment of topics from Abelian and non-Abelian
Nielsen Theory integrated with the semiconjugacy theorems of Franks and Handel.
The main focus is to develop an analog of the rotation set that is valid when
the dynamics are not isotopic to the identity and to connect this theory to the
dynamical persistence under homotopy/isotopy intrinsic in the theorems of
Franks and Handel. For this dynamical persistence, expansion/hyperbolicity at
some scale is essential.
