In the first part of the thesis , we study two one - dimensional dynamical systems with negative schwarzian derivative . by using the non - existence of attractive periodic orbits and wandering intervals , a theorem is obtained that the forward invariant compact sets of the two dynamical systems are uniform hyperbolic 本文第一部分主要考慮兩類具有負schwarz導數的單峰映射的動力學性質,利用吸引周期軌道和游蕩區間的不存在性等,證明了其正向不變緊集的一致雙曲性。