Review of dynamical complexity research based on topological horseshoe theory

Now, the research of dynamical complexity has become very popular, especially the analysis of the chaos. The chaotic character is obtained mainly by calculated Lyapunov exponents; however it is probably bad in some situations, so people want to have more rigorous arguments on existence of chaos. This paper reviews the topological horseshoe theory first, and then offered a rigorous chaotic analysis by means of topological horseshoe theory, at last, show the research papers on this topic.