Lehmer's question, knots and surface dynamics
  Lehmer's question is equivalent to one about generalized growth rates of Lefschetz numbers of iterated pseudo-Anosov surface homeomorphisms. One need consider only homeomorphisms that arise as monodromies of fibered knots in lens spaces L(n,1), n>0. Lehmer's question for Perron polynomials is equivalent to one about generalized growth rates of words under injective free group endomorphisms. 
Daniel S. Silver and Susan G. Williams