Li Yang's doctoral thesis has made an important contribution to the field of mathematics. First of all, his research involves complex network theory, which is a very important field in modern science. Through the study of complex networks, he revealed some important characteristics of networks, such as degree distribution and clustering coefficient, which is of great significance for understanding the structure and dynamic behavior of networks.

Secondly, his research also involves the theory of dynamic system, which is widely used in physics, biology, economics and other fields. Through the study of dynamic systems, he put forward a new method to understand and predict the dynamic behavior of complex systems, which has important guiding significance for solving many practical problems.

In addition, his research also involves topology, which is a very important branch of mathematics. Through the study of topology, he proposed a new method to understand and describe the spatial structure, which has important implications for solving many geometric and topological problems.

Generally speaking, Li Yang's doctoral thesis has made important contributions to the field of mathematics. His research results not only enrich our understanding of complex networks, dynamical systems and topology, but also provide new ideas and methods for solving many practical problems. Therefore, his research is of great significance for promoting the development of mathematics.