On Some Dynamical Properties Of Some One-dimensional Systems

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.In the second part of the thesis, we consider a one-dimensional dynamical system with only one discontinuous-critical point and prove that the set of periodic points is uniform hyperbolic if such a map is globally expanding.Han Shuguang (Dynamic System & Ergodic Theory)Directed by Prof. Cao Yongluo...