Characterizations of Morse quasi-geodesics via superlinear divergence   and sublinear contraction
  We introduce and begin a systematic study of sublinearly contracting projections. We give two characterizations of Morse quasi-geodesics in an arbitrary geodesic metric space. One is that they are sublinearly contracting; the other is that they have completely superlinear divergence. We give a further characterization of sublinearly contracting projections in terms of projections of geodesic segments. 
Goulnara N. Arzhantseva and Christopher H. Cashen and Dominik Gruber   and David Hume
math.MG math.GR