Characterizations of dominated splitting system and its relation to   hyperbolicity
  Hyperbolicity and dominated splitting are two of the most important concepts in the global analysis of differentiable dynamics. In this paper we give several equivalent characterizations of the dominated splitting and in particular we show a criterion for dynamical systems being dominated splitting in terms of hyperbolicity.18 pages 
Chun Fang, Mats Gyllenberg and Shitao Liu
math.DS