The Chaotic Dynamics For A Class Of Lorenz-type Maps

In this thesis, we investigate the chaotic dynamics for a class of Lorenz-type maps. We organize it into three sections.Section1is the introduction of the two definitions of chaos, the Li-Yorke chaos and Devaney chaos. Two methods, symbolic coding method and the topological entropy, are also listed in this section.Section2describes the chaotic dynamics for the Lorenz-type map. Firstly, by Markov partition, we get a transition matrix and the corresponding symbolic sub-space. Then we prove that the Lorenz-type map is topologically semi-conjugate to the sub-shift map on the symbolic space. Secondly, based on the preimages of the discontinuous point, we obtain an invariant set of the Lorenz-type map. This invariant set is a Cantor set in the sense of an order on S2. Further, we prove that the Lorenz-type map is conjugate to the shift map on E2. Finally, by simple computation, the topological entropy of sub-shift map is nonnegative.Section3is some general results for the Lorenz-type map.